diff --git a/internal/protocol/stream.go b/internal/protocol/stream.go
index 1735a235..988dcc82 100644
--- a/internal/protocol/stream.go
+++ b/internal/protocol/stream.go
@@ -1,19 +1,5 @@
 package protocol
 
-// A StreamID in QUIC
-type StreamID int64
-
-// InvalidPacketNumber is a stream ID that is invalid.
-// The first valid stream ID in QUIC is 0.
-const InvalidStreamID StreamID = -1
-
-// StreamNum is the stream number
-type StreamNum int64
-
-// MaxStreamCount is the maximum stream count value that can be sent in MAX_STREAMS frames
-// and as the stream count in the transport parameters
-const MaxStreamCount StreamNum = 1 << 60
-
 // StreamType encodes if this is a unidirectional or bidirectional stream
 type StreamType uint8
 
@@ -24,6 +10,49 @@ const (
 	StreamTypeBidi
 )
 
+// InvalidPacketNumber is a stream ID that is invalid.
+// The first valid stream ID in QUIC is 0.
+const InvalidStreamID StreamID = -1
+
+// StreamNum is the stream number
+type StreamNum int64
+
+const (
+	// InvalidStreamNum is an invalid stream number.
+	InvalidStreamNum = -1
+	// MaxStreamCount is the maximum stream count value that can be sent in MAX_STREAMS frames
+	// and as the stream count in the transport parameters
+	MaxStreamCount StreamNum = 1 << 60
+)
+
+// StreamID calculates the stream ID.
+func (s StreamNum) StreamID(stype StreamType, pers Perspective) StreamID {
+	if s == 0 {
+		return InvalidStreamID
+	}
+	var first StreamID
+	switch stype {
+	case StreamTypeBidi:
+		switch pers {
+		case PerspectiveClient:
+			first = 0
+		case PerspectiveServer:
+			first = 1
+		}
+	case StreamTypeUni:
+		switch pers {
+		case PerspectiveClient:
+			first = 2
+		case PerspectiveServer:
+			first = 3
+		}
+	}
+	return first + 4*StreamID(s-1)
+}
+
+// A StreamID in QUIC
+type StreamID int64
+
 // InitiatedBy says if the stream was initiated by the client or by the server
 func (s StreamID) InitiatedBy() Perspective {
 	if s%2 == 0 {
@@ -45,34 +74,3 @@ func (s StreamID) Type() StreamType {
 func (s StreamID) StreamNum() StreamNum {
 	return StreamNum(s/4) + 1
 }
-
-// MaxStreamID is the highest stream ID that a peer is allowed to open,
-// when it is allowed to open numStreams.
-func MaxStreamID(stype StreamType, numStreams StreamNum, pers Perspective) StreamID {
-	if numStreams == 0 {
-		return InvalidStreamID
-	}
-	var first StreamID
-	switch stype {
-	case StreamTypeBidi:
-		switch pers {
-		case PerspectiveClient:
-			first = 0
-		case PerspectiveServer:
-			first = 1
-		}
-	case StreamTypeUni:
-		switch pers {
-		case PerspectiveClient:
-			first = 2
-		case PerspectiveServer:
-			first = 3
-		}
-	}
-	return first + 4*StreamID(numStreams-1)
-}
-
-// FirstStream returns the first valid stream ID
-func FirstStream(stype StreamType, pers Perspective) StreamID {
-	return MaxStreamID(stype, 1, pers)
-}
diff --git a/internal/protocol/stream_test.go b/internal/protocol/stream_test.go
index eb9eea85..a8d4654c 100644
--- a/internal/protocol/stream_test.go
+++ b/internal/protocol/stream_test.go
@@ -24,13 +24,6 @@ var _ = Describe("Stream ID", func() {
 		Expect(StreamID(7).Type()).To(Equal(StreamTypeUni))
 	})
 
-	It("tells the first stream ID", func() {
-		Expect(FirstStream(StreamTypeBidi, PerspectiveClient)).To(Equal(StreamID(0)))
-		Expect(FirstStream(StreamTypeBidi, PerspectiveServer)).To(Equal(StreamID(1)))
-		Expect(FirstStream(StreamTypeUni, PerspectiveClient)).To(Equal(StreamID(2)))
-		Expect(FirstStream(StreamTypeUni, PerspectiveServer)).To(Equal(StreamID(3)))
-	})
-
 	It("tells the stream number", func() {
 		Expect(StreamID(0).StreamNum()).To(BeEquivalentTo(1))
 		Expect(StreamID(1).StreamNum()).To(BeEquivalentTo(1))
@@ -42,26 +35,26 @@ var _ = Describe("Stream ID", func() {
 		Expect(StreamID(11).StreamNum()).To(BeEquivalentTo(3))
 	})
 
-	Context("maximum stream IDs", func() {
-		It("doesn't allow any", func() {
-			Expect(MaxStreamID(StreamTypeBidi, 0, PerspectiveClient)).To(Equal(InvalidStreamID))
-			Expect(MaxStreamID(StreamTypeBidi, 0, PerspectiveServer)).To(Equal(InvalidStreamID))
-			Expect(MaxStreamID(StreamTypeUni, 0, PerspectiveClient)).To(Equal(InvalidStreamID))
-			Expect(MaxStreamID(StreamTypeUni, 0, PerspectiveServer)).To(Equal(InvalidStreamID))
+	Context("converting stream nums to stream IDs", func() {
+		It("handles 0", func() {
+			Expect(StreamNum(0).StreamID(StreamTypeBidi, PerspectiveClient)).To(Equal(InvalidStreamID))
+			Expect(StreamNum(0).StreamID(StreamTypeBidi, PerspectiveServer)).To(Equal(InvalidStreamID))
+			Expect(StreamNum(0).StreamID(StreamTypeUni, PerspectiveClient)).To(Equal(InvalidStreamID))
+			Expect(StreamNum(0).StreamID(StreamTypeUni, PerspectiveServer)).To(Equal(InvalidStreamID))
 		})
 
-		It("allows one", func() {
-			Expect(MaxStreamID(StreamTypeBidi, 1, PerspectiveClient)).To(Equal(StreamID(0)))
-			Expect(MaxStreamID(StreamTypeBidi, 1, PerspectiveServer)).To(Equal(StreamID(1)))
-			Expect(MaxStreamID(StreamTypeUni, 1, PerspectiveClient)).To(Equal(StreamID(2)))
-			Expect(MaxStreamID(StreamTypeUni, 1, PerspectiveServer)).To(Equal(StreamID(3)))
+		It("handles the first", func() {
+			Expect(StreamNum(1).StreamID(StreamTypeBidi, PerspectiveClient)).To(Equal(StreamID(0)))
+			Expect(StreamNum(1).StreamID(StreamTypeBidi, PerspectiveServer)).To(Equal(StreamID(1)))
+			Expect(StreamNum(1).StreamID(StreamTypeUni, PerspectiveClient)).To(Equal(StreamID(2)))
+			Expect(StreamNum(1).StreamID(StreamTypeUni, PerspectiveServer)).To(Equal(StreamID(3)))
 		})
 
-		It("allows many", func() {
-			Expect(MaxStreamID(StreamTypeBidi, 100, PerspectiveClient)).To(Equal(StreamID(396)))
-			Expect(MaxStreamID(StreamTypeBidi, 100, PerspectiveServer)).To(Equal(StreamID(397)))
-			Expect(MaxStreamID(StreamTypeUni, 100, PerspectiveClient)).To(Equal(StreamID(398)))
-			Expect(MaxStreamID(StreamTypeUni, 100, PerspectiveServer)).To(Equal(StreamID(399)))
+		It("handles others", func() {
+			Expect(StreamNum(100).StreamID(StreamTypeBidi, PerspectiveClient)).To(Equal(StreamID(396)))
+			Expect(StreamNum(100).StreamID(StreamTypeBidi, PerspectiveServer)).To(Equal(StreamID(397)))
+			Expect(StreamNum(100).StreamID(StreamTypeUni, PerspectiveClient)).To(Equal(StreamID(398)))
+			Expect(StreamNum(100).StreamID(StreamTypeUni, PerspectiveServer)).To(Equal(StreamID(399)))
 		})
 	})
 })
diff --git a/streams_map.go b/streams_map.go
index f4b9d581..cc53efd1 100644
--- a/streams_map.go
+++ b/streams_map.go
@@ -12,6 +12,27 @@ import (
 	"github.com/lucas-clemente/quic-go/internal/wire"
 )
 
+type streamError struct {
+	message string
+	nums    []protocol.StreamNum
+}
+
+func (e streamError) Error() string {
+	return e.message
+}
+
+func convertStreamError(err error, stype protocol.StreamType, pers protocol.Perspective) error {
+	strError, ok := err.(streamError)
+	if !ok {
+		return err
+	}
+	ids := make([]interface{}, len(strError.nums))
+	for i, num := range strError.nums {
+		ids[i] = num.StreamID(stype, pers)
+	}
+	return fmt.Errorf(strError.Error(), ids...)
+}
+
 type streamOpenErr struct{ error }
 
 var _ net.Error = &streamOpenErr{}
@@ -49,112 +70,144 @@ func newStreamsMap(
 		newFlowController: newFlowController,
 		sender:            sender,
 	}
-	newBidiStream := func(id protocol.StreamID) streamI {
-		return newStream(id, m.sender, m.newFlowController(id), version)
-	}
-	newUniSendStream := func(id protocol.StreamID) sendStreamI {
-		return newSendStream(id, m.sender, m.newFlowController(id), version)
-	}
-	newUniReceiveStream := func(id protocol.StreamID) receiveStreamI {
-		return newReceiveStream(id, m.sender, m.newFlowController(id), version)
-	}
 	m.outgoingBidiStreams = newOutgoingBidiStreamsMap(
-		protocol.FirstStream(protocol.StreamTypeBidi, perspective),
-		newBidiStream,
+		func(num protocol.StreamNum) streamI {
+			id := num.StreamID(protocol.StreamTypeBidi, perspective)
+			return newStream(id, m.sender, m.newFlowController(id), version)
+		},
 		sender.queueControlFrame,
 	)
 	m.incomingBidiStreams = newIncomingBidiStreamsMap(
-		protocol.FirstStream(protocol.StreamTypeBidi, perspective.Opposite()),
-		protocol.MaxStreamID(protocol.StreamTypeBidi, protocol.StreamNum(maxIncomingBidiStreams), perspective.Opposite()),
+		func(num protocol.StreamNum) streamI {
+			id := num.StreamID(protocol.StreamTypeBidi, perspective.Opposite())
+			return newStream(id, m.sender, m.newFlowController(id), version)
+		},
 		maxIncomingBidiStreams,
 		sender.queueControlFrame,
-		newBidiStream,
 	)
 	m.outgoingUniStreams = newOutgoingUniStreamsMap(
-		protocol.FirstStream(protocol.StreamTypeUni, perspective),
-		newUniSendStream,
+		func(num protocol.StreamNum) sendStreamI {
+			id := num.StreamID(protocol.StreamTypeUni, perspective)
+			return newSendStream(id, m.sender, m.newFlowController(id), version)
+		},
 		sender.queueControlFrame,
 	)
 	m.incomingUniStreams = newIncomingUniStreamsMap(
-		protocol.FirstStream(protocol.StreamTypeUni, perspective.Opposite()),
-		protocol.MaxStreamID(protocol.StreamTypeUni, protocol.StreamNum(maxIncomingUniStreams), perspective.Opposite()),
+		func(num protocol.StreamNum) receiveStreamI {
+			id := num.StreamID(protocol.StreamTypeUni, perspective.Opposite())
+			return newReceiveStream(id, m.sender, m.newFlowController(id), version)
+		},
 		maxIncomingUniStreams,
 		sender.queueControlFrame,
-		newUniReceiveStream,
 	)
 	return m
 }
 
 func (m *streamsMap) OpenStream() (Stream, error) {
-	return m.outgoingBidiStreams.OpenStream()
+	str, err := m.outgoingBidiStreams.OpenStream()
+	return str, convertStreamError(err, protocol.StreamTypeBidi, m.perspective)
 }
 
 func (m *streamsMap) OpenStreamSync() (Stream, error) {
-	return m.outgoingBidiStreams.OpenStreamSync()
+	str, err := m.outgoingBidiStreams.OpenStreamSync()
+	return str, convertStreamError(err, protocol.StreamTypeBidi, m.perspective)
 }
 
 func (m *streamsMap) OpenUniStream() (SendStream, error) {
-	return m.outgoingUniStreams.OpenStream()
+	str, err := m.outgoingUniStreams.OpenStream()
+	return str, convertStreamError(err, protocol.StreamTypeBidi, m.perspective)
 }
 
 func (m *streamsMap) OpenUniStreamSync() (SendStream, error) {
-	return m.outgoingUniStreams.OpenStreamSync()
+	str, err := m.outgoingUniStreams.OpenStreamSync()
+	return str, convertStreamError(err, protocol.StreamTypeUni, m.perspective)
 }
 
 func (m *streamsMap) AcceptStream() (Stream, error) {
-	return m.incomingBidiStreams.AcceptStream()
+	str, err := m.incomingBidiStreams.AcceptStream()
+	return str, convertStreamError(err, protocol.StreamTypeBidi, m.perspective.Opposite())
 }
 
 func (m *streamsMap) AcceptUniStream() (ReceiveStream, error) {
-	return m.incomingUniStreams.AcceptStream()
+	str, err := m.incomingUniStreams.AcceptStream()
+	return str, convertStreamError(err, protocol.StreamTypeUni, m.perspective.Opposite())
 }
 
 func (m *streamsMap) DeleteStream(id protocol.StreamID) error {
+	num := id.StreamNum()
 	switch id.Type() {
 	case protocol.StreamTypeUni:
 		if id.InitiatedBy() == m.perspective {
-			return m.outgoingUniStreams.DeleteStream(id)
+			return m.outgoingUniStreams.DeleteStream(num)
 		}
-		return m.incomingUniStreams.DeleteStream(id)
+		return m.incomingUniStreams.DeleteStream(num)
 	case protocol.StreamTypeBidi:
 		if id.InitiatedBy() == m.perspective {
-			return m.outgoingBidiStreams.DeleteStream(id)
+			return m.outgoingBidiStreams.DeleteStream(num)
 		}
-		return m.incomingBidiStreams.DeleteStream(id)
+		return m.incomingBidiStreams.DeleteStream(num)
 	}
 	panic("")
 }
 
 func (m *streamsMap) GetOrOpenReceiveStream(id protocol.StreamID) (receiveStreamI, error) {
+	str, err := m.getOrOpenReceiveStream(id)
+	if err != nil {
+		return nil, qerr.Error(qerr.StreamStateError, err.Error())
+	}
+	return str, nil
+}
+
+func (m *streamsMap) getOrOpenReceiveStream(id protocol.StreamID) (receiveStreamI, error) {
+	num := id.StreamNum()
 	switch id.Type() {
 	case protocol.StreamTypeUni:
 		if id.InitiatedBy() == m.perspective {
 			// an outgoing unidirectional stream is a send stream, not a receive stream
 			return nil, fmt.Errorf("peer attempted to open receive stream %d", id)
 		}
-		return m.incomingUniStreams.GetOrOpenStream(id)
+		str, err := m.incomingUniStreams.GetOrOpenStream(num)
+		return str, convertStreamError(err, protocol.StreamTypeUni, m.perspective)
 	case protocol.StreamTypeBidi:
+		var str receiveStreamI
+		var err error
 		if id.InitiatedBy() == m.perspective {
-			return m.outgoingBidiStreams.GetStream(id)
+			str, err = m.outgoingBidiStreams.GetStream(num)
+		} else {
+			str, err = m.incomingBidiStreams.GetOrOpenStream(num)
 		}
-		return m.incomingBidiStreams.GetOrOpenStream(id)
+		return str, convertStreamError(err, protocol.StreamTypeBidi, id.InitiatedBy())
 	}
 	panic("")
 }
 
 func (m *streamsMap) GetOrOpenSendStream(id protocol.StreamID) (sendStreamI, error) {
+	str, err := m.getOrOpenSendStream(id)
+	if err != nil {
+		return nil, qerr.Error(qerr.StreamStateError, err.Error())
+	}
+	return str, nil
+}
+
+func (m *streamsMap) getOrOpenSendStream(id protocol.StreamID) (sendStreamI, error) {
+	num := id.StreamNum()
 	switch id.Type() {
 	case protocol.StreamTypeUni:
 		if id.InitiatedBy() == m.perspective {
-			return m.outgoingUniStreams.GetStream(id)
+			str, err := m.outgoingUniStreams.GetStream(num)
+			return str, convertStreamError(err, protocol.StreamTypeUni, m.perspective)
 		}
 		// an incoming unidirectional stream is a receive stream, not a send stream
 		return nil, fmt.Errorf("peer attempted to open send stream %d", id)
 	case protocol.StreamTypeBidi:
+		var str sendStreamI
+		var err error
 		if id.InitiatedBy() == m.perspective {
-			return m.outgoingBidiStreams.GetStream(id)
+			str, err = m.outgoingBidiStreams.GetStream(num)
+		} else {
+			str, err = m.incomingBidiStreams.GetOrOpenStream(num)
 		}
-		return m.incomingBidiStreams.GetOrOpenStream(id)
+		return str, convertStreamError(err, protocol.StreamTypeBidi, id.InitiatedBy())
 	}
 	panic("")
 }
@@ -163,12 +216,11 @@ func (m *streamsMap) HandleMaxStreamsFrame(f *wire.MaxStreamsFrame) error {
 	if f.MaxStreamNum > protocol.MaxStreamCount {
 		return qerr.StreamLimitError
 	}
-	id := protocol.MaxStreamID(f.Type, f.MaxStreamNum, m.perspective)
-	switch id.Type() {
+	switch f.Type {
 	case protocol.StreamTypeUni:
-		m.outgoingUniStreams.SetMaxStream(id)
+		m.outgoingUniStreams.SetMaxStream(f.MaxStreamNum)
 	case protocol.StreamTypeBidi:
-		m.outgoingBidiStreams.SetMaxStream(id)
+		m.outgoingBidiStreams.SetMaxStream(f.MaxStreamNum)
 	}
 	return nil
 }
@@ -179,8 +231,8 @@ func (m *streamsMap) UpdateLimits(p *handshake.TransportParameters) error {
 		return qerr.StreamLimitError
 	}
 	// Max{Uni,Bidi}StreamID returns the highest stream ID that the peer is allowed to open.
-	m.outgoingBidiStreams.SetMaxStream(protocol.MaxStreamID(protocol.StreamTypeBidi, p.MaxBidiStreamNum, m.perspective))
-	m.outgoingUniStreams.SetMaxStream(protocol.MaxStreamID(protocol.StreamTypeUni, p.MaxUniStreamNum, m.perspective))
+	m.outgoingBidiStreams.SetMaxStream(p.MaxBidiStreamNum)
+	m.outgoingUniStreams.SetMaxStream(p.MaxUniStreamNum)
 	return nil
 }
 
diff --git a/streams_map_incoming_bidi.go b/streams_map_incoming_bidi.go
index 76f8cb8f..f0aad6a2 100644
--- a/streams_map_incoming_bidi.go
+++ b/streams_map_incoming_bidi.go
@@ -5,7 +5,6 @@
 package quic
 
 import (
-	"fmt"
 	"sync"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
@@ -16,38 +15,39 @@ type incomingBidiStreamsMap struct {
 	mutex sync.RWMutex
 	cond  sync.Cond
 
-	streams map[protocol.StreamID]streamI
+	streams map[protocol.StreamNum]streamI
 	// When a stream is deleted before it was accepted, we can't delete it immediately.
 	// We need to wait until the application accepts it, and delete it immediately then.
-	streamsToDelete map[protocol.StreamID]struct{} // used as a set
+	streamsToDelete map[protocol.StreamNum]struct{} // used as a set
 
-	nextStreamToAccept protocol.StreamID // the next stream that will be returned by AcceptStream()
-	nextStreamToOpen   protocol.StreamID // the highest stream that the peer openend
-	maxStream          protocol.StreamID // the highest stream that the peer is allowed to open
-	maxNumStreams      uint64            // maximum number of streams
+	nextStreamToAccept protocol.StreamNum // the next stream that will be returned by AcceptStream()
+	nextStreamToOpen   protocol.StreamNum // the highest stream that the peer openend
+	maxStream          protocol.StreamNum // the highest stream that the peer is allowed to open
+	maxNumStreams      uint64             // maximum number of streams
 
-	newStream        func(protocol.StreamID) streamI
+	newStream        func(protocol.StreamNum) streamI
 	queueMaxStreamID func(*wire.MaxStreamsFrame)
+	// streamNumToID    func(protocol.StreamNum) protocol.StreamID // only used for generating errors
 
 	closeErr error
 }
 
 func newIncomingBidiStreamsMap(
-	nextStreamToAccept protocol.StreamID,
-	initialMaxStreamID protocol.StreamID,
-	maxNumStreams uint64,
+	newStream func(protocol.StreamNum) streamI,
+	maxStreams uint64,
 	queueControlFrame func(wire.Frame),
-	newStream func(protocol.StreamID) streamI,
+	// streamNumToID func(protocol.StreamNum) protocol.StreamID,
 ) *incomingBidiStreamsMap {
 	m := &incomingBidiStreamsMap{
-		streams:            make(map[protocol.StreamID]streamI),
-		streamsToDelete:    make(map[protocol.StreamID]struct{}),
-		nextStreamToAccept: nextStreamToAccept,
-		nextStreamToOpen:   nextStreamToAccept,
-		maxStream:          initialMaxStreamID,
-		maxNumStreams:      maxNumStreams,
+		streams:            make(map[protocol.StreamNum]streamI),
+		streamsToDelete:    make(map[protocol.StreamNum]struct{}),
+		maxStream:          protocol.StreamNum(maxStreams),
+		maxNumStreams:      maxStreams,
 		newStream:          newStream,
+		nextStreamToOpen:   1,
+		nextStreamToAccept: 1,
 		queueMaxStreamID:   func(f *wire.MaxStreamsFrame) { queueControlFrame(f) },
+		// streamNumToID:      streamNumToID,
 	}
 	m.cond.L = &m.mutex
 	return m
@@ -57,45 +57,48 @@ func (m *incomingBidiStreamsMap) AcceptStream() (streamI, error) {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	var id protocol.StreamID
+	var num protocol.StreamNum
 	var str streamI
 	for {
-		id = m.nextStreamToAccept
+		num = m.nextStreamToAccept
 		var ok bool
 		if m.closeErr != nil {
 			return nil, m.closeErr
 		}
-		str, ok = m.streams[id]
+		str, ok = m.streams[num]
 		if ok {
 			break
 		}
 		m.cond.Wait()
 	}
-	m.nextStreamToAccept += 4
+	m.nextStreamToAccept++
 	// If this stream was completed before being accepted, we can delete it now.
-	if _, ok := m.streamsToDelete[id]; ok {
-		delete(m.streamsToDelete, id)
-		if err := m.deleteStream(id); err != nil {
+	if _, ok := m.streamsToDelete[num]; ok {
+		delete(m.streamsToDelete, num)
+		if err := m.deleteStream(num); err != nil {
 			return nil, err
 		}
 	}
 	return str, nil
 }
 
-func (m *incomingBidiStreamsMap) GetOrOpenStream(id protocol.StreamID) (streamI, error) {
+func (m *incomingBidiStreamsMap) GetOrOpenStream(num protocol.StreamNum) (streamI, error) {
 	m.mutex.RLock()
-	if id > m.maxStream {
+	if num > m.maxStream {
 		m.mutex.RUnlock()
-		return nil, fmt.Errorf("peer tried to open stream %d (current limit: %d)", id, m.maxStream)
+		return nil, streamError{
+			message: "peer tried to open stream %d (current limit: %d)",
+			nums:    []protocol.StreamNum{num, m.maxStream},
+		}
 	}
-	// if the id is smaller than the highest we accepted
+	// if the num is smaller than the highest we accepted
 	// * this stream exists in the map, and we can return it, or
 	// * this stream was already closed, then we can return the nil
-	if id < m.nextStreamToOpen {
+	if num < m.nextStreamToOpen {
 		var s streamI
 		// If the stream was already queued for deletion, and is just waiting to be accepted, don't return it.
-		if _, ok := m.streamsToDelete[id]; !ok {
-			s = m.streams[id]
+		if _, ok := m.streamsToDelete[num]; !ok {
+			s = m.streams[num]
 		}
 		m.mutex.RUnlock()
 		return s, nil
@@ -106,46 +109,52 @@ func (m *incomingBidiStreamsMap) GetOrOpenStream(id protocol.StreamID) (streamI,
 	// no need to check the two error conditions from above again
 	// * maxStream can only increase, so if the id was valid before, it definitely is valid now
 	// * highestStream is only modified by this function
-	for newID := m.nextStreamToOpen; newID <= id; newID += 4 {
-		m.streams[newID] = m.newStream(newID)
+	for newNum := m.nextStreamToOpen; newNum <= num; newNum++ {
+		m.streams[newNum] = m.newStream(newNum)
 		m.cond.Signal()
 	}
-	m.nextStreamToOpen = id + 4
-	s := m.streams[id]
+	m.nextStreamToOpen = num + 1
+	s := m.streams[num]
 	m.mutex.Unlock()
 	return s, nil
 }
 
-func (m *incomingBidiStreamsMap) DeleteStream(id protocol.StreamID) error {
+func (m *incomingBidiStreamsMap) DeleteStream(num protocol.StreamNum) error {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	return m.deleteStream(id)
+	return m.deleteStream(num)
 }
 
-func (m *incomingBidiStreamsMap) deleteStream(id protocol.StreamID) error {
-	if _, ok := m.streams[id]; !ok {
-		return fmt.Errorf("Tried to delete unknown stream %d", id)
+func (m *incomingBidiStreamsMap) deleteStream(num protocol.StreamNum) error {
+	if _, ok := m.streams[num]; !ok {
+		return streamError{
+			message: "Tried to delete unknown stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
 
 	// Don't delete this stream yet, if it was not yet accepted.
 	// Just save it to streamsToDelete map, to make sure it is deleted as soon as it gets accepted.
-	if id >= m.nextStreamToAccept {
-		if _, ok := m.streamsToDelete[id]; ok {
-			return fmt.Errorf("Tried to delete stream %d multiple times", id)
+	if num >= m.nextStreamToAccept {
+		if _, ok := m.streamsToDelete[num]; ok {
+			return streamError{
+				message: "Tried to delete stream %d multiple times",
+				nums:    []protocol.StreamNum{num},
+			}
 		}
-		m.streamsToDelete[id] = struct{}{}
+		m.streamsToDelete[num] = struct{}{}
 		return nil
 	}
 
-	delete(m.streams, id)
+	delete(m.streams, num)
 	// queue a MAX_STREAM_ID frame, giving the peer the option to open a new stream
 	if m.maxNumStreams > uint64(len(m.streams)) {
 		numNewStreams := m.maxNumStreams - uint64(len(m.streams))
-		m.maxStream = m.nextStreamToOpen + protocol.StreamID((numNewStreams-1)*4)
+		m.maxStream = m.nextStreamToOpen + protocol.StreamNum(numNewStreams) - 1
 		m.queueMaxStreamID(&wire.MaxStreamsFrame{
 			Type:         protocol.StreamTypeBidi,
-			MaxStreamNum: m.maxStream.StreamNum(),
+			MaxStreamNum: m.maxStream,
 		})
 	}
 	return nil
diff --git a/streams_map_incoming_generic.go b/streams_map_incoming_generic.go
index 2d873db2..c7485aca 100644
--- a/streams_map_incoming_generic.go
+++ b/streams_map_incoming_generic.go
@@ -1,7 +1,6 @@
 package quic
 
 import (
-	"fmt"
 	"sync"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
@@ -14,38 +13,39 @@ type incomingItemsMap struct {
 	mutex sync.RWMutex
 	cond  sync.Cond
 
-	streams map[protocol.StreamID]item
+	streams map[protocol.StreamNum]item
 	// When a stream is deleted before it was accepted, we can't delete it immediately.
 	// We need to wait until the application accepts it, and delete it immediately then.
-	streamsToDelete map[protocol.StreamID]struct{} // used as a set
+	streamsToDelete map[protocol.StreamNum]struct{} // used as a set
 
-	nextStreamToAccept protocol.StreamID // the next stream that will be returned by AcceptStream()
-	nextStreamToOpen   protocol.StreamID // the highest stream that the peer openend
-	maxStream          protocol.StreamID // the highest stream that the peer is allowed to open
-	maxNumStreams      uint64            // maximum number of streams
+	nextStreamToAccept protocol.StreamNum // the next stream that will be returned by AcceptStream()
+	nextStreamToOpen   protocol.StreamNum // the highest stream that the peer openend
+	maxStream          protocol.StreamNum // the highest stream that the peer is allowed to open
+	maxNumStreams      uint64             // maximum number of streams
 
-	newStream        func(protocol.StreamID) item
+	newStream        func(protocol.StreamNum) item
 	queueMaxStreamID func(*wire.MaxStreamsFrame)
+	// streamNumToID    func(protocol.StreamNum) protocol.StreamID // only used for generating errors
 
 	closeErr error
 }
 
 func newIncomingItemsMap(
-	nextStreamToAccept protocol.StreamID,
-	initialMaxStreamID protocol.StreamID,
-	maxNumStreams uint64,
+	newStream func(protocol.StreamNum) item,
+	maxStreams uint64,
 	queueControlFrame func(wire.Frame),
-	newStream func(protocol.StreamID) item,
+	// streamNumToID func(protocol.StreamNum) protocol.StreamID,
 ) *incomingItemsMap {
 	m := &incomingItemsMap{
-		streams:            make(map[protocol.StreamID]item),
-		streamsToDelete:    make(map[protocol.StreamID]struct{}),
-		nextStreamToAccept: nextStreamToAccept,
-		nextStreamToOpen:   nextStreamToAccept,
-		maxStream:          initialMaxStreamID,
-		maxNumStreams:      maxNumStreams,
+		streams:            make(map[protocol.StreamNum]item),
+		streamsToDelete:    make(map[protocol.StreamNum]struct{}),
+		maxStream:          protocol.StreamNum(maxStreams),
+		maxNumStreams:      maxStreams,
 		newStream:          newStream,
+		nextStreamToOpen:   1,
+		nextStreamToAccept: 1,
 		queueMaxStreamID:   func(f *wire.MaxStreamsFrame) { queueControlFrame(f) },
+		// streamNumToID:      streamNumToID,
 	}
 	m.cond.L = &m.mutex
 	return m
@@ -55,45 +55,48 @@ func (m *incomingItemsMap) AcceptStream() (item, error) {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	var id protocol.StreamID
+	var num protocol.StreamNum
 	var str item
 	for {
-		id = m.nextStreamToAccept
+		num = m.nextStreamToAccept
 		var ok bool
 		if m.closeErr != nil {
 			return nil, m.closeErr
 		}
-		str, ok = m.streams[id]
+		str, ok = m.streams[num]
 		if ok {
 			break
 		}
 		m.cond.Wait()
 	}
-	m.nextStreamToAccept += 4
+	m.nextStreamToAccept++
 	// If this stream was completed before being accepted, we can delete it now.
-	if _, ok := m.streamsToDelete[id]; ok {
-		delete(m.streamsToDelete, id)
-		if err := m.deleteStream(id); err != nil {
+	if _, ok := m.streamsToDelete[num]; ok {
+		delete(m.streamsToDelete, num)
+		if err := m.deleteStream(num); err != nil {
 			return nil, err
 		}
 	}
 	return str, nil
 }
 
-func (m *incomingItemsMap) GetOrOpenStream(id protocol.StreamID) (item, error) {
+func (m *incomingItemsMap) GetOrOpenStream(num protocol.StreamNum) (item, error) {
 	m.mutex.RLock()
-	if id > m.maxStream {
+	if num > m.maxStream {
 		m.mutex.RUnlock()
-		return nil, fmt.Errorf("peer tried to open stream %d (current limit: %d)", id, m.maxStream)
+		return nil, streamError{
+			message: "peer tried to open stream %d (current limit: %d)",
+			nums:    []protocol.StreamNum{num, m.maxStream},
+		}
 	}
-	// if the id is smaller than the highest we accepted
+	// if the num is smaller than the highest we accepted
 	// * this stream exists in the map, and we can return it, or
 	// * this stream was already closed, then we can return the nil
-	if id < m.nextStreamToOpen {
+	if num < m.nextStreamToOpen {
 		var s item
 		// If the stream was already queued for deletion, and is just waiting to be accepted, don't return it.
-		if _, ok := m.streamsToDelete[id]; !ok {
-			s = m.streams[id]
+		if _, ok := m.streamsToDelete[num]; !ok {
+			s = m.streams[num]
 		}
 		m.mutex.RUnlock()
 		return s, nil
@@ -104,46 +107,52 @@ func (m *incomingItemsMap) GetOrOpenStream(id protocol.StreamID) (item, error) {
 	// no need to check the two error conditions from above again
 	// * maxStream can only increase, so if the id was valid before, it definitely is valid now
 	// * highestStream is only modified by this function
-	for newID := m.nextStreamToOpen; newID <= id; newID += 4 {
-		m.streams[newID] = m.newStream(newID)
+	for newNum := m.nextStreamToOpen; newNum <= num; newNum++ {
+		m.streams[newNum] = m.newStream(newNum)
 		m.cond.Signal()
 	}
-	m.nextStreamToOpen = id + 4
-	s := m.streams[id]
+	m.nextStreamToOpen = num + 1
+	s := m.streams[num]
 	m.mutex.Unlock()
 	return s, nil
 }
 
-func (m *incomingItemsMap) DeleteStream(id protocol.StreamID) error {
+func (m *incomingItemsMap) DeleteStream(num protocol.StreamNum) error {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	return m.deleteStream(id)
+	return m.deleteStream(num)
 }
 
-func (m *incomingItemsMap) deleteStream(id protocol.StreamID) error {
-	if _, ok := m.streams[id]; !ok {
-		return fmt.Errorf("Tried to delete unknown stream %d", id)
+func (m *incomingItemsMap) deleteStream(num protocol.StreamNum) error {
+	if _, ok := m.streams[num]; !ok {
+		return streamError{
+			message: "Tried to delete unknown stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
 
 	// Don't delete this stream yet, if it was not yet accepted.
 	// Just save it to streamsToDelete map, to make sure it is deleted as soon as it gets accepted.
-	if id >= m.nextStreamToAccept {
-		if _, ok := m.streamsToDelete[id]; ok {
-			return fmt.Errorf("Tried to delete stream %d multiple times", id)
+	if num >= m.nextStreamToAccept {
+		if _, ok := m.streamsToDelete[num]; ok {
+			return streamError{
+				message: "Tried to delete stream %d multiple times",
+				nums:    []protocol.StreamNum{num},
+			}
 		}
-		m.streamsToDelete[id] = struct{}{}
+		m.streamsToDelete[num] = struct{}{}
 		return nil
 	}
 
-	delete(m.streams, id)
+	delete(m.streams, num)
 	// queue a MAX_STREAM_ID frame, giving the peer the option to open a new stream
 	if m.maxNumStreams > uint64(len(m.streams)) {
 		numNewStreams := m.maxNumStreams - uint64(len(m.streams))
-		m.maxStream = m.nextStreamToOpen + protocol.StreamID((numNewStreams-1)*4)
+		m.maxStream = m.nextStreamToOpen + protocol.StreamNum(numNewStreams) - 1
 		m.queueMaxStreamID(&wire.MaxStreamsFrame{
 			Type:         streamTypeGeneric,
-			MaxStreamNum: m.maxStream.StreamNum(),
+			MaxStreamNum: m.maxStream,
 		})
 	}
 	return nil
diff --git a/streams_map_incoming_generic_test.go b/streams_map_incoming_generic_test.go
index 6f503c54..0a59b7f5 100644
--- a/streams_map_incoming_generic_test.go
+++ b/streams_map_incoming_generic_test.go
@@ -2,7 +2,6 @@ package quic
 
 import (
 	"errors"
-	"fmt"
 
 	"github.com/golang/mock/gomock"
 	"github.com/lucas-clemente/quic-go/internal/protocol"
@@ -13,7 +12,7 @@ import (
 )
 
 type mockGenericStream struct {
-	id protocol.StreamID
+	num protocol.StreamNum
 
 	closed   bool
 	closeErr error
@@ -26,64 +25,65 @@ func (s *mockGenericStream) closeForShutdown(err error) {
 
 var _ = Describe("Streams Map (incoming)", func() {
 	const (
-		firstNewStream   protocol.StreamID = 2
-		maxNumStreams    uint64            = 5
-		initialMaxStream protocol.StreamID = firstNewStream + 4*protocol.StreamID(maxNumStreams-1)
+		maxNumStreams uint64 = 5
 	)
 
 	var (
 		m              *incomingItemsMap
-		newItem        func(id protocol.StreamID) item
 		newItemCounter int
 		mockSender     *MockStreamSender
 	)
 
 	BeforeEach(func() {
 		newItemCounter = 0
-		newItem = func(id protocol.StreamID) item {
-			newItemCounter++
-			return &mockGenericStream{id: id}
-		}
 		mockSender = NewMockStreamSender(mockCtrl)
-		m = newIncomingItemsMap(firstNewStream, initialMaxStream, maxNumStreams, mockSender.queueControlFrame, newItem)
+		m = newIncomingItemsMap(
+			func(num protocol.StreamNum) item {
+				newItemCounter++
+				return &mockGenericStream{num: num}
+			},
+			maxNumStreams,
+			mockSender.queueControlFrame,
+		)
 	})
 
 	It("opens all streams up to the id on GetOrOpenStream", func() {
-		_, err := m.GetOrOpenStream(firstNewStream + 4*4)
+		_, err := m.GetOrOpenStream(4)
 		Expect(err).ToNot(HaveOccurred())
-		Expect(newItemCounter).To(Equal(5))
+		Expect(newItemCounter).To(Equal(4))
 	})
 
 	It("starts opening streams at the right position", func() {
 		// like the test above, but with 2 calls to GetOrOpenStream
-		_, err := m.GetOrOpenStream(firstNewStream + 4)
+		_, err := m.GetOrOpenStream(2)
 		Expect(err).ToNot(HaveOccurred())
 		Expect(newItemCounter).To(Equal(2))
-		_, err = m.GetOrOpenStream(firstNewStream + 4*4)
+		_, err = m.GetOrOpenStream(5)
 		Expect(err).ToNot(HaveOccurred())
 		Expect(newItemCounter).To(Equal(5))
 	})
 
 	It("accepts streams in the right order", func() {
-		_, err := m.GetOrOpenStream(firstNewStream + 4) // open stream 20 and 24
+		_, err := m.GetOrOpenStream(2) // open streams 1 and 2
 		Expect(err).ToNot(HaveOccurred())
 		str, err := m.AcceptStream()
 		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream))
+		Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 		str, err = m.AcceptStream()
 		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream + 4))
+		Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(2)))
 	})
 
 	It("allows opening the maximum stream ID", func() {
-		str, err := m.GetOrOpenStream(initialMaxStream)
+		str, err := m.GetOrOpenStream(1)
 		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(Equal(initialMaxStream))
+		Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 	})
 
 	It("errors when trying to get a stream ID higher than the maximum", func() {
-		_, err := m.GetOrOpenStream(initialMaxStream + 4)
-		Expect(err).To(MatchError(fmt.Errorf("peer tried to open stream %d (current limit: %d)", initialMaxStream+4, initialMaxStream)))
+		_, err := m.GetOrOpenStream(6)
+		Expect(err).To(HaveOccurred())
+		Expect(err.(streamError).TestError()).To(MatchError("peer tried to open stream 6 (current limit: 5)"))
 	})
 
 	It("blocks AcceptStream until a new stream is available", func() {
@@ -95,30 +95,12 @@ var _ = Describe("Streams Map (incoming)", func() {
 			strChan <- str
 		}()
 		Consistently(strChan).ShouldNot(Receive())
-		str, err := m.GetOrOpenStream(firstNewStream)
+		str, err := m.GetOrOpenStream(1)
 		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream))
+		Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 		var acceptedStr item
 		Eventually(strChan).Should(Receive(&acceptedStr))
-		Expect(acceptedStr.(*mockGenericStream).id).To(Equal(firstNewStream))
-	})
-
-	It("works with stream 0", func() {
-		m = newIncomingItemsMap(0, 1000, 1000, mockSender.queueControlFrame, newItem)
-		strChan := make(chan item)
-		go func() {
-			defer GinkgoRecover()
-			str, err := m.AcceptStream()
-			Expect(err).ToNot(HaveOccurred())
-			strChan <- str
-		}()
-		Consistently(strChan).ShouldNot(Receive())
-		str, err := m.GetOrOpenStream(0)
-		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(BeZero())
-		var acceptedStr item
-		Eventually(strChan).Should(Receive(&acceptedStr))
-		Expect(acceptedStr.(*mockGenericStream).id).To(BeZero())
+		Expect(acceptedStr.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 	})
 
 	It("unblocks AcceptStream when it is closed", func() {
@@ -143,9 +125,9 @@ var _ = Describe("Streams Map (incoming)", func() {
 	})
 
 	It("closes all streams when CloseWithError is called", func() {
-		str1, err := m.GetOrOpenStream(firstNewStream)
+		str1, err := m.GetOrOpenStream(1)
 		Expect(err).ToNot(HaveOccurred())
-		str2, err := m.GetOrOpenStream(firstNewStream + 8)
+		str2, err := m.GetOrOpenStream(3)
 		Expect(err).ToNot(HaveOccurred())
 		testErr := errors.New("test err")
 		m.CloseWithError(testErr)
@@ -157,37 +139,37 @@ var _ = Describe("Streams Map (incoming)", func() {
 
 	It("deletes streams", func() {
 		mockSender.EXPECT().queueControlFrame(gomock.Any())
-		_, err := m.GetOrOpenStream(firstNewStream)
+		_, err := m.GetOrOpenStream(1)
 		Expect(err).ToNot(HaveOccurred())
 		str, err := m.AcceptStream()
 		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream))
-		Expect(m.DeleteStream(firstNewStream)).To(Succeed())
-		str, err = m.GetOrOpenStream(firstNewStream)
+		Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
+		Expect(m.DeleteStream(1)).To(Succeed())
+		str, err = m.GetOrOpenStream(1)
 		Expect(err).ToNot(HaveOccurred())
 		Expect(str).To(BeNil())
 	})
 
 	It("waits until a stream is accepted before actually deleting it", func() {
-		_, err := m.GetOrOpenStream(firstNewStream + 4)
+		_, err := m.GetOrOpenStream(2)
 		Expect(err).ToNot(HaveOccurred())
-		Expect(m.DeleteStream(firstNewStream + 4)).To(Succeed())
+		Expect(m.DeleteStream(2)).To(Succeed())
 		str, err := m.AcceptStream()
 		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream))
+		Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 		// when accepting this stream, it will get deleted, and a MAX_STREAMS frame is queued
 		mockSender.EXPECT().queueControlFrame(gomock.Any())
 		str, err = m.AcceptStream()
 		Expect(err).ToNot(HaveOccurred())
-		Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream + 4))
+		Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(2)))
 	})
 
 	It("doesn't return a stream queued for deleting from GetOrOpenStream", func() {
-		str, err := m.GetOrOpenStream(firstNewStream)
+		str, err := m.GetOrOpenStream(1)
 		Expect(err).ToNot(HaveOccurred())
 		Expect(str).ToNot(BeNil())
-		Expect(m.DeleteStream(firstNewStream)).To(Succeed())
-		str, err = m.GetOrOpenStream(firstNewStream)
+		Expect(m.DeleteStream(1)).To(Succeed())
+		str, err = m.GetOrOpenStream(1)
 		Expect(err).ToNot(HaveOccurred())
 		Expect(str).To(BeNil())
 		// when accepting this stream, it will get deleted, and a MAX_STREAMS frame is queued
@@ -199,12 +181,13 @@ var _ = Describe("Streams Map (incoming)", func() {
 
 	It("errors when deleting a non-existing stream", func() {
 		err := m.DeleteStream(1337)
-		Expect(err).To(MatchError("Tried to delete unknown stream 1337"))
+		Expect(err).To(HaveOccurred())
+		Expect(err.(streamError).TestError()).To(MatchError("Tried to delete unknown stream 1337"))
 	})
 
 	It("sends MAX_STREAMS frames when streams are deleted", func() {
 		// open a bunch of streams
-		_, err := m.GetOrOpenStream(firstNewStream + 4*4)
+		_, err := m.GetOrOpenStream(5)
 		Expect(err).ToNot(HaveOccurred())
 		// accept all streams
 		for i := 0; i < 5; i++ {
@@ -214,10 +197,10 @@ var _ = Describe("Streams Map (incoming)", func() {
 		mockSender.EXPECT().queueControlFrame(gomock.Any()).Do(func(f wire.Frame) {
 			Expect(f.(*wire.MaxStreamsFrame).MaxStreamNum).To(Equal(protocol.StreamNum(maxNumStreams + 1)))
 		})
-		Expect(m.DeleteStream(firstNewStream + 2*4)).To(Succeed())
+		Expect(m.DeleteStream(3)).To(Succeed())
 		mockSender.EXPECT().queueControlFrame(gomock.Any()).Do(func(f wire.Frame) {
 			Expect(f.(*wire.MaxStreamsFrame).MaxStreamNum).To(Equal(protocol.StreamNum(maxNumStreams + 2)))
 		})
-		Expect(m.DeleteStream(firstNewStream + 3*4)).To(Succeed())
+		Expect(m.DeleteStream(4)).To(Succeed())
 	})
 })
diff --git a/streams_map_incoming_uni.go b/streams_map_incoming_uni.go
index 39ae05a2..cc83eb66 100644
--- a/streams_map_incoming_uni.go
+++ b/streams_map_incoming_uni.go
@@ -5,7 +5,6 @@
 package quic
 
 import (
-	"fmt"
 	"sync"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
@@ -16,38 +15,39 @@ type incomingUniStreamsMap struct {
 	mutex sync.RWMutex
 	cond  sync.Cond
 
-	streams map[protocol.StreamID]receiveStreamI
+	streams map[protocol.StreamNum]receiveStreamI
 	// When a stream is deleted before it was accepted, we can't delete it immediately.
 	// We need to wait until the application accepts it, and delete it immediately then.
-	streamsToDelete map[protocol.StreamID]struct{} // used as a set
+	streamsToDelete map[protocol.StreamNum]struct{} // used as a set
 
-	nextStreamToAccept protocol.StreamID // the next stream that will be returned by AcceptStream()
-	nextStreamToOpen   protocol.StreamID // the highest stream that the peer openend
-	maxStream          protocol.StreamID // the highest stream that the peer is allowed to open
-	maxNumStreams      uint64            // maximum number of streams
+	nextStreamToAccept protocol.StreamNum // the next stream that will be returned by AcceptStream()
+	nextStreamToOpen   protocol.StreamNum // the highest stream that the peer openend
+	maxStream          protocol.StreamNum // the highest stream that the peer is allowed to open
+	maxNumStreams      uint64             // maximum number of streams
 
-	newStream        func(protocol.StreamID) receiveStreamI
+	newStream        func(protocol.StreamNum) receiveStreamI
 	queueMaxStreamID func(*wire.MaxStreamsFrame)
+	// streamNumToID    func(protocol.StreamNum) protocol.StreamID // only used for generating errors
 
 	closeErr error
 }
 
 func newIncomingUniStreamsMap(
-	nextStreamToAccept protocol.StreamID,
-	initialMaxStreamID protocol.StreamID,
-	maxNumStreams uint64,
+	newStream func(protocol.StreamNum) receiveStreamI,
+	maxStreams uint64,
 	queueControlFrame func(wire.Frame),
-	newStream func(protocol.StreamID) receiveStreamI,
+	// streamNumToID func(protocol.StreamNum) protocol.StreamID,
 ) *incomingUniStreamsMap {
 	m := &incomingUniStreamsMap{
-		streams:            make(map[protocol.StreamID]receiveStreamI),
-		streamsToDelete:    make(map[protocol.StreamID]struct{}),
-		nextStreamToAccept: nextStreamToAccept,
-		nextStreamToOpen:   nextStreamToAccept,
-		maxStream:          initialMaxStreamID,
-		maxNumStreams:      maxNumStreams,
+		streams:            make(map[protocol.StreamNum]receiveStreamI),
+		streamsToDelete:    make(map[protocol.StreamNum]struct{}),
+		maxStream:          protocol.StreamNum(maxStreams),
+		maxNumStreams:      maxStreams,
 		newStream:          newStream,
+		nextStreamToOpen:   1,
+		nextStreamToAccept: 1,
 		queueMaxStreamID:   func(f *wire.MaxStreamsFrame) { queueControlFrame(f) },
+		// streamNumToID:      streamNumToID,
 	}
 	m.cond.L = &m.mutex
 	return m
@@ -57,45 +57,48 @@ func (m *incomingUniStreamsMap) AcceptStream() (receiveStreamI, error) {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	var id protocol.StreamID
+	var num protocol.StreamNum
 	var str receiveStreamI
 	for {
-		id = m.nextStreamToAccept
+		num = m.nextStreamToAccept
 		var ok bool
 		if m.closeErr != nil {
 			return nil, m.closeErr
 		}
-		str, ok = m.streams[id]
+		str, ok = m.streams[num]
 		if ok {
 			break
 		}
 		m.cond.Wait()
 	}
-	m.nextStreamToAccept += 4
+	m.nextStreamToAccept++
 	// If this stream was completed before being accepted, we can delete it now.
-	if _, ok := m.streamsToDelete[id]; ok {
-		delete(m.streamsToDelete, id)
-		if err := m.deleteStream(id); err != nil {
+	if _, ok := m.streamsToDelete[num]; ok {
+		delete(m.streamsToDelete, num)
+		if err := m.deleteStream(num); err != nil {
 			return nil, err
 		}
 	}
 	return str, nil
 }
 
-func (m *incomingUniStreamsMap) GetOrOpenStream(id protocol.StreamID) (receiveStreamI, error) {
+func (m *incomingUniStreamsMap) GetOrOpenStream(num protocol.StreamNum) (receiveStreamI, error) {
 	m.mutex.RLock()
-	if id > m.maxStream {
+	if num > m.maxStream {
 		m.mutex.RUnlock()
-		return nil, fmt.Errorf("peer tried to open stream %d (current limit: %d)", id, m.maxStream)
+		return nil, streamError{
+			message: "peer tried to open stream %d (current limit: %d)",
+			nums:    []protocol.StreamNum{num, m.maxStream},
+		}
 	}
-	// if the id is smaller than the highest we accepted
+	// if the num is smaller than the highest we accepted
 	// * this stream exists in the map, and we can return it, or
 	// * this stream was already closed, then we can return the nil
-	if id < m.nextStreamToOpen {
+	if num < m.nextStreamToOpen {
 		var s receiveStreamI
 		// If the stream was already queued for deletion, and is just waiting to be accepted, don't return it.
-		if _, ok := m.streamsToDelete[id]; !ok {
-			s = m.streams[id]
+		if _, ok := m.streamsToDelete[num]; !ok {
+			s = m.streams[num]
 		}
 		m.mutex.RUnlock()
 		return s, nil
@@ -106,46 +109,52 @@ func (m *incomingUniStreamsMap) GetOrOpenStream(id protocol.StreamID) (receiveSt
 	// no need to check the two error conditions from above again
 	// * maxStream can only increase, so if the id was valid before, it definitely is valid now
 	// * highestStream is only modified by this function
-	for newID := m.nextStreamToOpen; newID <= id; newID += 4 {
-		m.streams[newID] = m.newStream(newID)
+	for newNum := m.nextStreamToOpen; newNum <= num; newNum++ {
+		m.streams[newNum] = m.newStream(newNum)
 		m.cond.Signal()
 	}
-	m.nextStreamToOpen = id + 4
-	s := m.streams[id]
+	m.nextStreamToOpen = num + 1
+	s := m.streams[num]
 	m.mutex.Unlock()
 	return s, nil
 }
 
-func (m *incomingUniStreamsMap) DeleteStream(id protocol.StreamID) error {
+func (m *incomingUniStreamsMap) DeleteStream(num protocol.StreamNum) error {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	return m.deleteStream(id)
+	return m.deleteStream(num)
 }
 
-func (m *incomingUniStreamsMap) deleteStream(id protocol.StreamID) error {
-	if _, ok := m.streams[id]; !ok {
-		return fmt.Errorf("Tried to delete unknown stream %d", id)
+func (m *incomingUniStreamsMap) deleteStream(num protocol.StreamNum) error {
+	if _, ok := m.streams[num]; !ok {
+		return streamError{
+			message: "Tried to delete unknown stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
 
 	// Don't delete this stream yet, if it was not yet accepted.
 	// Just save it to streamsToDelete map, to make sure it is deleted as soon as it gets accepted.
-	if id >= m.nextStreamToAccept {
-		if _, ok := m.streamsToDelete[id]; ok {
-			return fmt.Errorf("Tried to delete stream %d multiple times", id)
+	if num >= m.nextStreamToAccept {
+		if _, ok := m.streamsToDelete[num]; ok {
+			return streamError{
+				message: "Tried to delete stream %d multiple times",
+				nums:    []protocol.StreamNum{num},
+			}
 		}
-		m.streamsToDelete[id] = struct{}{}
+		m.streamsToDelete[num] = struct{}{}
 		return nil
 	}
 
-	delete(m.streams, id)
+	delete(m.streams, num)
 	// queue a MAX_STREAM_ID frame, giving the peer the option to open a new stream
 	if m.maxNumStreams > uint64(len(m.streams)) {
 		numNewStreams := m.maxNumStreams - uint64(len(m.streams))
-		m.maxStream = m.nextStreamToOpen + protocol.StreamID((numNewStreams-1)*4)
+		m.maxStream = m.nextStreamToOpen + protocol.StreamNum(numNewStreams) - 1
 		m.queueMaxStreamID(&wire.MaxStreamsFrame{
 			Type:         protocol.StreamTypeUni,
-			MaxStreamNum: m.maxStream.StreamNum(),
+			MaxStreamNum: m.maxStream,
 		})
 	}
 	return nil
diff --git a/streams_map_outgoing_bidi.go b/streams_map_outgoing_bidi.go
index ca8727e6..bce33b52 100644
--- a/streams_map_outgoing_bidi.go
+++ b/streams_map_outgoing_bidi.go
@@ -5,11 +5,9 @@
 package quic
 
 import (
-	"fmt"
 	"sync"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
-	"github.com/lucas-clemente/quic-go/internal/qerr"
 	"github.com/lucas-clemente/quic-go/internal/wire"
 )
 
@@ -17,27 +15,26 @@ type outgoingBidiStreamsMap struct {
 	mutex sync.RWMutex
 	cond  sync.Cond
 
-	streams map[protocol.StreamID]streamI
+	streams map[protocol.StreamNum]streamI
 
-	nextStream  protocol.StreamID // stream ID of the stream returned by OpenStream(Sync)
-	maxStream   protocol.StreamID // the maximum stream ID we're allowed to open
-	blockedSent bool              // was a STREAMS_BLOCKED sent for the current maxStream
+	nextStream  protocol.StreamNum // stream ID of the stream returned by OpenStream(Sync)
+	maxStream   protocol.StreamNum // the maximum stream ID we're allowed to open
+	blockedSent bool               // was a STREAMS_BLOCKED sent for the current maxStream
 
-	newStream            func(protocol.StreamID) streamI
+	newStream            func(protocol.StreamNum) streamI
 	queueStreamIDBlocked func(*wire.StreamsBlockedFrame)
 
 	closeErr error
 }
 
 func newOutgoingBidiStreamsMap(
-	nextStream protocol.StreamID,
-	newStream func(protocol.StreamID) streamI,
+	newStream func(protocol.StreamNum) streamI,
 	queueControlFrame func(wire.Frame),
 ) *outgoingBidiStreamsMap {
 	m := &outgoingBidiStreamsMap{
-		streams:              make(map[protocol.StreamID]streamI),
-		nextStream:           nextStream,
-		maxStream:            protocol.InvalidStreamID,
+		streams:              make(map[protocol.StreamNum]streamI),
+		maxStream:            protocol.InvalidStreamNum,
+		nextStream:           1,
 		newStream:            newStream,
 		queueStreamIDBlocked: func(f *wire.StreamsBlockedFrame) { queueControlFrame(f) },
 	}
@@ -83,8 +80,8 @@ func (m *outgoingBidiStreamsMap) openStreamImpl() (streamI, error) {
 	if m.nextStream > m.maxStream {
 		if !m.blockedSent {
 			var streamNum protocol.StreamNum
-			if m.maxStream != protocol.InvalidStreamID {
-				streamNum = m.maxStream.StreamNum()
+			if m.maxStream != protocol.InvalidStreamNum {
+				streamNum = m.maxStream
 			}
 			m.queueStreamIDBlocked(&wire.StreamsBlockedFrame{
 				Type:        protocol.StreamTypeBidi,
@@ -96,36 +93,42 @@ func (m *outgoingBidiStreamsMap) openStreamImpl() (streamI, error) {
 	}
 	s := m.newStream(m.nextStream)
 	m.streams[m.nextStream] = s
-	m.nextStream += 4
+	m.nextStream++
 	return s, nil
 }
 
-func (m *outgoingBidiStreamsMap) GetStream(id protocol.StreamID) (streamI, error) {
+func (m *outgoingBidiStreamsMap) GetStream(num protocol.StreamNum) (streamI, error) {
 	m.mutex.RLock()
-	if id >= m.nextStream {
+	if num >= m.nextStream {
 		m.mutex.RUnlock()
-		return nil, qerr.Error(qerr.StreamStateError, fmt.Sprintf("peer attempted to open stream %d", id))
+		return nil, streamError{
+			message: "peer attempted to open stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
-	s := m.streams[id]
+	s := m.streams[num]
 	m.mutex.RUnlock()
 	return s, nil
 }
 
-func (m *outgoingBidiStreamsMap) DeleteStream(id protocol.StreamID) error {
+func (m *outgoingBidiStreamsMap) DeleteStream(num protocol.StreamNum) error {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	if _, ok := m.streams[id]; !ok {
-		return fmt.Errorf("Tried to delete unknown stream %d", id)
+	if _, ok := m.streams[num]; !ok {
+		return streamError{
+			message: "Tried to delete unknown stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
-	delete(m.streams, id)
+	delete(m.streams, num)
 	return nil
 }
 
-func (m *outgoingBidiStreamsMap) SetMaxStream(id protocol.StreamID) {
+func (m *outgoingBidiStreamsMap) SetMaxStream(num protocol.StreamNum) {
 	m.mutex.Lock()
-	if id > m.maxStream {
-		m.maxStream = id
+	if num > m.maxStream {
+		m.maxStream = num
 		m.blockedSent = false
 		m.cond.Broadcast()
 	}
diff --git a/streams_map_outgoing_generic.go b/streams_map_outgoing_generic.go
index 4fcf0471..3fc04a4d 100644
--- a/streams_map_outgoing_generic.go
+++ b/streams_map_outgoing_generic.go
@@ -1,11 +1,9 @@
 package quic
 
 import (
-	"fmt"
 	"sync"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
-	"github.com/lucas-clemente/quic-go/internal/qerr"
 	"github.com/lucas-clemente/quic-go/internal/wire"
 )
 
@@ -15,27 +13,26 @@ type outgoingItemsMap struct {
 	mutex sync.RWMutex
 	cond  sync.Cond
 
-	streams map[protocol.StreamID]item
+	streams map[protocol.StreamNum]item
 
-	nextStream  protocol.StreamID // stream ID of the stream returned by OpenStream(Sync)
-	maxStream   protocol.StreamID // the maximum stream ID we're allowed to open
-	blockedSent bool              // was a STREAMS_BLOCKED sent for the current maxStream
+	nextStream  protocol.StreamNum // stream ID of the stream returned by OpenStream(Sync)
+	maxStream   protocol.StreamNum // the maximum stream ID we're allowed to open
+	blockedSent bool               // was a STREAMS_BLOCKED sent for the current maxStream
 
-	newStream            func(protocol.StreamID) item
+	newStream            func(protocol.StreamNum) item
 	queueStreamIDBlocked func(*wire.StreamsBlockedFrame)
 
 	closeErr error
 }
 
 func newOutgoingItemsMap(
-	nextStream protocol.StreamID,
-	newStream func(protocol.StreamID) item,
+	newStream func(protocol.StreamNum) item,
 	queueControlFrame func(wire.Frame),
 ) *outgoingItemsMap {
 	m := &outgoingItemsMap{
-		streams:              make(map[protocol.StreamID]item),
-		nextStream:           nextStream,
-		maxStream:            protocol.InvalidStreamID,
+		streams:              make(map[protocol.StreamNum]item),
+		maxStream:            protocol.InvalidStreamNum,
+		nextStream:           1,
 		newStream:            newStream,
 		queueStreamIDBlocked: func(f *wire.StreamsBlockedFrame) { queueControlFrame(f) },
 	}
@@ -81,8 +78,8 @@ func (m *outgoingItemsMap) openStreamImpl() (item, error) {
 	if m.nextStream > m.maxStream {
 		if !m.blockedSent {
 			var streamNum protocol.StreamNum
-			if m.maxStream != protocol.InvalidStreamID {
-				streamNum = m.maxStream.StreamNum()
+			if m.maxStream != protocol.InvalidStreamNum {
+				streamNum = m.maxStream
 			}
 			m.queueStreamIDBlocked(&wire.StreamsBlockedFrame{
 				Type:        streamTypeGeneric,
@@ -94,36 +91,42 @@ func (m *outgoingItemsMap) openStreamImpl() (item, error) {
 	}
 	s := m.newStream(m.nextStream)
 	m.streams[m.nextStream] = s
-	m.nextStream += 4
+	m.nextStream++
 	return s, nil
 }
 
-func (m *outgoingItemsMap) GetStream(id protocol.StreamID) (item, error) {
+func (m *outgoingItemsMap) GetStream(num protocol.StreamNum) (item, error) {
 	m.mutex.RLock()
-	if id >= m.nextStream {
+	if num >= m.nextStream {
 		m.mutex.RUnlock()
-		return nil, qerr.Error(qerr.StreamStateError, fmt.Sprintf("peer attempted to open stream %d", id))
+		return nil, streamError{
+			message: "peer attempted to open stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
-	s := m.streams[id]
+	s := m.streams[num]
 	m.mutex.RUnlock()
 	return s, nil
 }
 
-func (m *outgoingItemsMap) DeleteStream(id protocol.StreamID) error {
+func (m *outgoingItemsMap) DeleteStream(num protocol.StreamNum) error {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	if _, ok := m.streams[id]; !ok {
-		return fmt.Errorf("Tried to delete unknown stream %d", id)
+	if _, ok := m.streams[num]; !ok {
+		return streamError{
+			message: "Tried to delete unknown stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
-	delete(m.streams, id)
+	delete(m.streams, num)
 	return nil
 }
 
-func (m *outgoingItemsMap) SetMaxStream(id protocol.StreamID) {
+func (m *outgoingItemsMap) SetMaxStream(num protocol.StreamNum) {
 	m.mutex.Lock()
-	if id > m.maxStream {
-		m.maxStream = id
+	if num > m.maxStream {
+		m.maxStream = num
 		m.blockedSent = false
 		m.cond.Broadcast()
 	}
diff --git a/streams_map_outgoing_generic_test.go b/streams_map_outgoing_generic_test.go
index 5ab66089..9779a901 100644
--- a/streams_map_outgoing_generic_test.go
+++ b/streams_map_outgoing_generic_test.go
@@ -5,27 +5,24 @@ import (
 
 	"github.com/golang/mock/gomock"
 	"github.com/lucas-clemente/quic-go/internal/protocol"
-	"github.com/lucas-clemente/quic-go/internal/qerr"
 	"github.com/lucas-clemente/quic-go/internal/wire"
 	. "github.com/onsi/ginkgo"
 	. "github.com/onsi/gomega"
 )
 
 var _ = Describe("Streams Map (outgoing)", func() {
-	const firstNewStream protocol.StreamID = 3
-
 	var (
 		m          *outgoingItemsMap
-		newItem    func(id protocol.StreamID) item
+		newItem    func(num protocol.StreamNum) item
 		mockSender *MockStreamSender
 	)
 
 	BeforeEach(func() {
-		newItem = func(id protocol.StreamID) item {
-			return &mockGenericStream{id: id}
+		newItem = func(num protocol.StreamNum) item {
+			return &mockGenericStream{num: num}
 		}
 		mockSender = NewMockStreamSender(mockCtrl)
-		m = newOutgoingItemsMap(firstNewStream, newItem, mockSender.queueControlFrame)
+		m = newOutgoingItemsMap(newItem, mockSender.queueControlFrame)
 	})
 
 	Context("no stream ID limit", func() {
@@ -36,10 +33,10 @@ var _ = Describe("Streams Map (outgoing)", func() {
 		It("opens streams", func() {
 			str, err := m.OpenStream()
 			Expect(err).ToNot(HaveOccurred())
-			Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream))
+			Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 			str, err = m.OpenStream()
 			Expect(err).ToNot(HaveOccurred())
-			Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream + 4))
+			Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(2)))
 		})
 
 		It("doesn't open streams after it has been closed", func() {
@@ -52,38 +49,40 @@ var _ = Describe("Streams Map (outgoing)", func() {
 		It("gets streams", func() {
 			_, err := m.OpenStream()
 			Expect(err).ToNot(HaveOccurred())
-			str, err := m.GetStream(firstNewStream)
+			str, err := m.GetStream(1)
 			Expect(err).ToNot(HaveOccurred())
-			Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream))
+			Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 		})
 
 		It("errors when trying to get a stream that has not yet been opened", func() {
-			_, err := m.GetStream(firstNewStream)
-			Expect(err).To(MatchError(qerr.Error(qerr.StreamStateError, "peer attempted to open stream 3")))
+			_, err := m.GetStream(1)
+			Expect(err).To(HaveOccurred())
+			Expect(err.(streamError).TestError()).To(MatchError("peer attempted to open stream 1"))
 		})
 
 		It("deletes streams", func() {
-			_, err := m.OpenStream() // opens firstNewStream
+			_, err := m.OpenStream()
 			Expect(err).ToNot(HaveOccurred())
-			err = m.DeleteStream(firstNewStream)
+			Expect(m.DeleteStream(1)).To(Succeed())
 			Expect(err).ToNot(HaveOccurred())
-			str, err := m.GetStream(firstNewStream)
+			str, err := m.GetStream(1)
 			Expect(err).ToNot(HaveOccurred())
 			Expect(str).To(BeNil())
 		})
 
 		It("errors when deleting a non-existing stream", func() {
 			err := m.DeleteStream(1337)
-			Expect(err).To(MatchError("Tried to delete unknown stream 1337"))
+			Expect(err).To(HaveOccurred())
+			Expect(err.(streamError).TestError()).To(MatchError("Tried to delete unknown stream 1337"))
 		})
 
 		It("errors when deleting a stream twice", func() {
 			_, err := m.OpenStream() // opens firstNewStream
 			Expect(err).ToNot(HaveOccurred())
-			err = m.DeleteStream(firstNewStream)
-			Expect(err).ToNot(HaveOccurred())
-			err = m.DeleteStream(firstNewStream)
-			Expect(err).To(MatchError("Tried to delete unknown stream 3"))
+			Expect(m.DeleteStream(1)).To(Succeed())
+			err = m.DeleteStream(1)
+			Expect(err).To(HaveOccurred())
+			Expect(err.(streamError).TestError()).To(MatchError("Tried to delete unknown stream 1"))
 		})
 
 		It("closes all streams when CloseWithError is called", func() {
@@ -114,31 +113,12 @@ var _ = Describe("Streams Map (outgoing)", func() {
 				defer GinkgoRecover()
 				str, err := m.OpenStreamSync()
 				Expect(err).ToNot(HaveOccurred())
-				Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream))
+				Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(1)))
 				close(done)
 			}()
 
 			Consistently(done).ShouldNot(BeClosed())
-			m.SetMaxStream(firstNewStream)
-			Eventually(done).Should(BeClosed())
-		})
-
-		It("works with stream 0", func() {
-			m = newOutgoingItemsMap(0, newItem, mockSender.queueControlFrame)
-			mockSender.EXPECT().queueControlFrame(gomock.Any()).Do(func(f wire.Frame) {
-				Expect(f.(*wire.StreamsBlockedFrame).StreamLimit).To(BeZero())
-			})
-			done := make(chan struct{})
-			go func() {
-				defer GinkgoRecover()
-				str, err := m.OpenStreamSync()
-				Expect(err).ToNot(HaveOccurred())
-				Expect(str.(*mockGenericStream).id).To(BeZero())
-				close(done)
-			}()
-
-			Consistently(done).ShouldNot(BeClosed())
-			m.SetMaxStream(0)
+			m.SetMaxStream(1)
 			Eventually(done).Should(BeClosed())
 		})
 
@@ -159,17 +139,17 @@ var _ = Describe("Streams Map (outgoing)", func() {
 		})
 
 		It("doesn't reduce the stream limit", func() {
-			m.SetMaxStream(firstNewStream + 4)
-			m.SetMaxStream(firstNewStream)
+			m.SetMaxStream(2)
+			m.SetMaxStream(1)
 			_, err := m.OpenStream()
 			Expect(err).ToNot(HaveOccurred())
 			str, err := m.OpenStream()
 			Expect(err).ToNot(HaveOccurred())
-			Expect(str.(*mockGenericStream).id).To(Equal(firstNewStream + 4))
+			Expect(str.(*mockGenericStream).num).To(Equal(protocol.StreamNum(2)))
 		})
 
 		It("queues a STREAM_ID_BLOCKED frame if no stream can be opened", func() {
-			m.SetMaxStream(firstNewStream + 5*4)
+			m.SetMaxStream(6)
 			// open the 6 allowed streams
 			for i := 0; i < 6; i++ {
 				_, err := m.OpenStream()
@@ -185,7 +165,7 @@ var _ = Describe("Streams Map (outgoing)", func() {
 		})
 
 		It("only sends one STREAM_ID_BLOCKED frame for one stream ID", func() {
-			m.SetMaxStream(firstNewStream)
+			m.SetMaxStream(1)
 			mockSender.EXPECT().queueControlFrame(gomock.Any()).Do(func(f wire.Frame) {
 				Expect(f.(*wire.StreamsBlockedFrame).StreamLimit).To(BeEquivalentTo(1))
 			})
diff --git a/streams_map_outgoing_uni.go b/streams_map_outgoing_uni.go
index 42befdaa..3ed98ff5 100644
--- a/streams_map_outgoing_uni.go
+++ b/streams_map_outgoing_uni.go
@@ -5,11 +5,9 @@
 package quic
 
 import (
-	"fmt"
 	"sync"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
-	"github.com/lucas-clemente/quic-go/internal/qerr"
 	"github.com/lucas-clemente/quic-go/internal/wire"
 )
 
@@ -17,27 +15,26 @@ type outgoingUniStreamsMap struct {
 	mutex sync.RWMutex
 	cond  sync.Cond
 
-	streams map[protocol.StreamID]sendStreamI
+	streams map[protocol.StreamNum]sendStreamI
 
-	nextStream  protocol.StreamID // stream ID of the stream returned by OpenStream(Sync)
-	maxStream   protocol.StreamID // the maximum stream ID we're allowed to open
-	blockedSent bool              // was a STREAMS_BLOCKED sent for the current maxStream
+	nextStream  protocol.StreamNum // stream ID of the stream returned by OpenStream(Sync)
+	maxStream   protocol.StreamNum // the maximum stream ID we're allowed to open
+	blockedSent bool               // was a STREAMS_BLOCKED sent for the current maxStream
 
-	newStream            func(protocol.StreamID) sendStreamI
+	newStream            func(protocol.StreamNum) sendStreamI
 	queueStreamIDBlocked func(*wire.StreamsBlockedFrame)
 
 	closeErr error
 }
 
 func newOutgoingUniStreamsMap(
-	nextStream protocol.StreamID,
-	newStream func(protocol.StreamID) sendStreamI,
+	newStream func(protocol.StreamNum) sendStreamI,
 	queueControlFrame func(wire.Frame),
 ) *outgoingUniStreamsMap {
 	m := &outgoingUniStreamsMap{
-		streams:              make(map[protocol.StreamID]sendStreamI),
-		nextStream:           nextStream,
-		maxStream:            protocol.InvalidStreamID,
+		streams:              make(map[protocol.StreamNum]sendStreamI),
+		maxStream:            protocol.InvalidStreamNum,
+		nextStream:           1,
 		newStream:            newStream,
 		queueStreamIDBlocked: func(f *wire.StreamsBlockedFrame) { queueControlFrame(f) },
 	}
@@ -83,8 +80,8 @@ func (m *outgoingUniStreamsMap) openStreamImpl() (sendStreamI, error) {
 	if m.nextStream > m.maxStream {
 		if !m.blockedSent {
 			var streamNum protocol.StreamNum
-			if m.maxStream != protocol.InvalidStreamID {
-				streamNum = m.maxStream.StreamNum()
+			if m.maxStream != protocol.InvalidStreamNum {
+				streamNum = m.maxStream
 			}
 			m.queueStreamIDBlocked(&wire.StreamsBlockedFrame{
 				Type:        protocol.StreamTypeUni,
@@ -96,36 +93,42 @@ func (m *outgoingUniStreamsMap) openStreamImpl() (sendStreamI, error) {
 	}
 	s := m.newStream(m.nextStream)
 	m.streams[m.nextStream] = s
-	m.nextStream += 4
+	m.nextStream++
 	return s, nil
 }
 
-func (m *outgoingUniStreamsMap) GetStream(id protocol.StreamID) (sendStreamI, error) {
+func (m *outgoingUniStreamsMap) GetStream(num protocol.StreamNum) (sendStreamI, error) {
 	m.mutex.RLock()
-	if id >= m.nextStream {
+	if num >= m.nextStream {
 		m.mutex.RUnlock()
-		return nil, qerr.Error(qerr.StreamStateError, fmt.Sprintf("peer attempted to open stream %d", id))
+		return nil, streamError{
+			message: "peer attempted to open stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
-	s := m.streams[id]
+	s := m.streams[num]
 	m.mutex.RUnlock()
 	return s, nil
 }
 
-func (m *outgoingUniStreamsMap) DeleteStream(id protocol.StreamID) error {
+func (m *outgoingUniStreamsMap) DeleteStream(num protocol.StreamNum) error {
 	m.mutex.Lock()
 	defer m.mutex.Unlock()
 
-	if _, ok := m.streams[id]; !ok {
-		return fmt.Errorf("Tried to delete unknown stream %d", id)
+	if _, ok := m.streams[num]; !ok {
+		return streamError{
+			message: "Tried to delete unknown stream %d",
+			nums:    []protocol.StreamNum{num},
+		}
 	}
-	delete(m.streams, id)
+	delete(m.streams, num)
 	return nil
 }
 
-func (m *outgoingUniStreamsMap) SetMaxStream(id protocol.StreamID) {
+func (m *outgoingUniStreamsMap) SetMaxStream(num protocol.StreamNum) {
 	m.mutex.Lock()
-	if id > m.maxStream {
-		m.maxStream = id
+	if num > m.maxStream {
+		m.maxStream = num
 		m.blockedSent = false
 		m.cond.Broadcast()
 	}
diff --git a/streams_map_test.go b/streams_map_test.go
index 5b233de6..cbace466 100644
--- a/streams_map_test.go
+++ b/streams_map_test.go
@@ -17,6 +17,14 @@ import (
 	. "github.com/onsi/gomega"
 )
 
+func (e streamError) TestError() error {
+	nums := make([]interface{}, len(e.nums))
+	for i, num := range e.nums {
+		nums[i] = num
+	}
+	return fmt.Errorf(e.message, nums...)
+}
+
 type streamMapping struct {
 	firstIncomingBidiStream protocol.StreamID
 	firstIncomingUniStream  protocol.StreamID
@@ -221,7 +229,7 @@ var _ = Describe("Streams Map", func() {
 					It("errors when the peer tries to open a higher outgoing bidirectional stream", func() {
 						id := ids.firstOutgoingBidiStream + 5*4
 						_, err := m.GetOrOpenSendStream(id)
-						Expect(err).To(MatchError(qerr.Error(qerr.StreamStateError, fmt.Sprintf("peer attempted to open stream %d", id))))
+						Expect(err).To(MatchError(fmt.Sprintf("STREAM_STATE_ERROR: peer attempted to open stream %d", id)))
 					})
 
 					It("gets an outgoing unidirectional stream", func() {
@@ -237,7 +245,7 @@ var _ = Describe("Streams Map", func() {
 					It("errors when the peer tries to open a higher outgoing bidirectional stream", func() {
 						id := ids.firstOutgoingUniStream + 5*4
 						_, err := m.GetOrOpenSendStream(id)
-						Expect(err).To(MatchError(qerr.Error(qerr.StreamStateError, fmt.Sprintf("peer attempted to open stream %d", id))))
+						Expect(err).To(MatchError(fmt.Sprintf("STREAM_STATE_ERROR: peer attempted to open stream %d", id)))
 					})
 
 					It("gets an incoming bidirectional stream", func() {
@@ -250,7 +258,7 @@ var _ = Describe("Streams Map", func() {
 					It("errors when trying to get an incoming unidirectional stream", func() {
 						id := ids.firstIncomingUniStream
 						_, err := m.GetOrOpenSendStream(id)
-						Expect(err).To(MatchError(fmt.Errorf("peer attempted to open send stream %d", id)))
+						Expect(err).To(MatchError(fmt.Sprintf("STREAM_STATE_ERROR: peer attempted to open send stream %d", id)))
 					})
 				})
 
@@ -268,7 +276,7 @@ var _ = Describe("Streams Map", func() {
 					It("errors when the peer tries to open a higher outgoing bidirectional stream", func() {
 						id := ids.firstOutgoingBidiStream + 5*4
 						_, err := m.GetOrOpenReceiveStream(id)
-						Expect(err).To(MatchError(qerr.Error(qerr.StreamStateError, fmt.Sprintf("peer attempted to open stream %d", id))))
+						Expect(err).To(MatchError(fmt.Sprintf("STREAM_STATE_ERROR: peer attempted to open stream %d", id)))
 					})
 
 					It("gets an incoming bidirectional stream", func() {
@@ -288,37 +296,44 @@ var _ = Describe("Streams Map", func() {
 					It("errors when trying to get an outgoing unidirectional stream", func() {
 						id := ids.firstOutgoingUniStream
 						_, err := m.GetOrOpenReceiveStream(id)
-						Expect(err).To(MatchError(fmt.Errorf("peer attempted to open receive stream %d", id)))
+						Expect(err).To(MatchError(fmt.Sprintf("STREAM_STATE_ERROR: peer attempted to open receive stream %d", id)))
 					})
 				})
 			})
 
 			Context("updating stream ID limits", func() {
-				It("processes the parameter for outgoing streams, as a server", func() {
-					mockSender.EXPECT().queueControlFrame(gomock.Any())
-					m.perspective = protocol.PerspectiveServer
-					_, err := m.OpenStream()
-					expectTooManyStreamsError(err)
-					Expect(m.UpdateLimits(&handshake.TransportParameters{
-						MaxBidiStreamNum: 5,
-						MaxUniStreamNum:  5,
-					})).To(Succeed())
-					Expect(m.outgoingBidiStreams.maxStream).To(Equal(protocol.StreamID(17)))
-					Expect(m.outgoingUniStreams.maxStream).To(Equal(protocol.StreamID(19)))
-				})
+				for _, p := range []protocol.Perspective{protocol.PerspectiveClient, protocol.PerspectiveServer} {
+					pers := p
 
-				It("processes the parameter for outgoing streams, as a client", func() {
-					mockSender.EXPECT().queueControlFrame(gomock.Any())
-					m.perspective = protocol.PerspectiveClient
-					_, err := m.OpenUniStream()
-					expectTooManyStreamsError(err)
-					Expect(m.UpdateLimits(&handshake.TransportParameters{
-						MaxBidiStreamNum: 5,
-						MaxUniStreamNum:  5,
-					})).To(Succeed())
-					Expect(m.outgoingBidiStreams.maxStream).To(Equal(protocol.StreamID(16)))
-					Expect(m.outgoingUniStreams.maxStream).To(Equal(protocol.StreamID(18)))
-				})
+					It(fmt.Sprintf("processes the parameter for outgoing streams, as a %s", pers), func() {
+						mockSender.EXPECT().queueControlFrame(gomock.Any())
+						m.perspective = pers
+						_, err := m.OpenStream()
+						expectTooManyStreamsError(err)
+						Expect(m.UpdateLimits(&handshake.TransportParameters{
+							MaxBidiStreamNum: 5,
+							MaxUniStreamNum:  8,
+						})).To(Succeed())
+
+						mockSender.EXPECT().queueControlFrame(gomock.Any()).Times(2)
+						// test we can only 5 bidirectional streams
+						for i := 0; i < 5; i++ {
+							str, err := m.OpenStream()
+							Expect(err).ToNot(HaveOccurred())
+							Expect(str.StreamID()).To(Equal(ids.firstOutgoingBidiStream + protocol.StreamID(4*i)))
+						}
+						_, err = m.OpenStream()
+						expectTooManyStreamsError(err)
+						// test we can only 8 unidirectional streams
+						for i := 0; i < 8; i++ {
+							str, err := m.OpenUniStream()
+							Expect(err).ToNot(HaveOccurred())
+							Expect(str.StreamID()).To(Equal(ids.firstOutgoingUniStream + protocol.StreamID(4*i)))
+						}
+						_, err = m.OpenUniStream()
+						expectTooManyStreamsError(err)
+					})
+				}
 
 				It("rejects parameters with too large unidirectional stream counts", func() {
 					Expect(m.UpdateLimits(&handshake.TransportParameters{