diff --git a/streams_map.go b/streams_map.go
index 05ce1a390..0bb2a200f 100644
--- a/streams_map.go
+++ b/streams_map.go
@@ -7,17 +7,15 @@ import (
 
 	"github.com/lucas-clemente/quic-go/protocol"
 	"github.com/lucas-clemente/quic-go/qerr"
-)
-
-const (
-	maxNumStreams = int(float32(protocol.MaxStreamsPerConnection) * protocol.MaxStreamsMultiplier)
+	"github.com/lucas-clemente/quic-go/utils"
 )
 
 type streamsMap struct {
-	streams     map[protocol.StreamID]*stream
-	openStreams []protocol.StreamID
-	mutex       sync.RWMutex
-	newStream   newStreamLambda
+	streams       map[protocol.StreamID]*stream
+	openStreams   []protocol.StreamID
+	mutex         sync.RWMutex
+	newStream     newStreamLambda
+	maxNumStreams int
 
 	roundRobinIndex int
 }
@@ -30,10 +28,13 @@ var (
 )
 
 func newStreamsMap(newStream newStreamLambda) *streamsMap {
+	maxNumStreams := utils.Max(int(float32(protocol.MaxIncomingDynamicStreams)*protocol.MaxStreamsMultiplier), int(protocol.MaxIncomingDynamicStreams))
+
 	return &streamsMap{
-		streams:     map[protocol.StreamID]*stream{},
-		openStreams: make([]protocol.StreamID, 0, maxNumStreams),
-		newStream:   newStream,
+		streams:       map[protocol.StreamID]*stream{},
+		openStreams:   make([]protocol.StreamID, 0, maxNumStreams),
+		newStream:     newStream,
+		maxNumStreams: maxNumStreams,
 	}
 }
 
@@ -54,7 +55,7 @@ func (m *streamsMap) GetOrOpenStream(id protocol.StreamID) (*stream, error) {
 	if ok {
 		return s, nil
 	}
-	if len(m.openStreams) == maxNumStreams {
+	if len(m.openStreams) == m.maxNumStreams {
 		return nil, qerr.TooManyOpenStreams
 	}
 	if id%2 == 0 {
diff --git a/streams_map_test.go b/streams_map_test.go
index 4e04a559a..ddd772a7d 100644
--- a/streams_map_test.go
+++ b/streams_map_test.go
@@ -60,16 +60,16 @@ var _ = Describe("Streams Map", func() {
 
 		Context("counting streams", func() {
 			It("errors when too many streams are opened", func() {
-				for i := 0; i < maxNumStreams; i++ {
+				for i := 0; i < m.maxNumStreams; i++ {
 					_, err := m.GetOrOpenStream(protocol.StreamID(i*2 + 1))
 					Expect(err).NotTo(HaveOccurred())
 				}
-				_, err := m.GetOrOpenStream(protocol.StreamID(maxNumStreams))
+				_, err := m.GetOrOpenStream(protocol.StreamID(m.maxNumStreams))
 				Expect(err).To(MatchError(qerr.TooManyOpenStreams))
 			})
 
 			It("does not error when many streams are opened and closed", func() {
-				for i := 2; i < 10*maxNumStreams; i++ {
+				for i := 2; i < 10*m.maxNumStreams; i++ {
 					_, err := m.GetOrOpenStream(protocol.StreamID(i*2 + 1))
 					Expect(err).NotTo(HaveOccurred())
 					m.RemoveStream(protocol.StreamID(i*2 + 1))