diff --git a/session.go b/session.go
index 67d44654..68eb8fab 100644
--- a/session.go
+++ b/session.go
@@ -61,6 +61,15 @@ type receivedPacket struct {
 	buffer *packetBuffer
 }
 
+func (p *receivedPacket) Clone() *receivedPacket {
+	return &receivedPacket{
+		remoteAddr: p.remoteAddr,
+		rcvTime:    p.rcvTime,
+		data:       p.data,
+		buffer:     p.buffer,
+	}
+}
+
 type closeError struct {
 	err       error
 	remote    bool
@@ -487,11 +496,18 @@ func (s *session) handleHandshakeComplete() {
 	}
 }
 
-func (s *session) handlePacketImpl(p *receivedPacket) bool {
+func (s *session) handlePacketImpl(rp *receivedPacket) bool {
 	var counter uint8
 	var lastConnID protocol.ConnectionID
 	var processed bool
-	for len(p.data) > 0 {
+	data := rp.data
+	p := rp
+	for len(data) > 0 {
+		if counter > 0 {
+			p = p.Clone()
+			p.data = data
+		}
+
 		hdr, packetData, rest, err := wire.ParsePacket(p.data, s.srcConnID.Len())
 		if err != nil {
 			s.logger.Debugf("error parsing packet: %s", err)
@@ -514,11 +530,10 @@ func (s *session) handlePacketImpl(p *receivedPacket) bool {
 			s.logger.Debugf("Parsed a coalesced packet. Part %d: %d bytes. Remaining: %d bytes.", counter, len(packetData), len(rest))
 		}
 		p.data = packetData
-		pr := s.handleSinglePacket(p, hdr)
-		if pr {
-			processed = pr
+		if wasProcessed := s.handleSinglePacket(p, hdr); wasProcessed {
+			processed = true
 		}
-		p.data = rest
+		data = rest
 	}
 	p.buffer.MaybeRelease()
 	return processed
@@ -744,6 +759,7 @@ func (s *session) handleCryptoFrame(frame *wire.CryptoFrame, encLevel protocol.E
 	if err != nil {
 		return err
 	}
+	s.logger.Debugf("Handled crypto frame at level %s. encLevelChanged: %t", encLevel, encLevelChanged)
 	if encLevelChanged {
 		s.tryDecryptingQueuedPackets()
 	}
diff --git a/session_test.go b/session_test.go
index af5e6be2..9e17a1e9 100644
--- a/session_test.go
+++ b/session_test.go
@@ -632,6 +632,25 @@ var _ = Describe("Session", func() {
 			Expect(sess.handlePacketImpl(getPacket(hdr2, nil))).To(BeFalse())
 		})
 
+		It("queues undecryptable packets", func() {
+			hdr := &wire.ExtendedHeader{
+				Header: wire.Header{
+					IsLongHeader:     true,
+					Type:             protocol.PacketTypeHandshake,
+					DestConnectionID: sess.destConnID,
+					SrcConnectionID:  sess.srcConnID,
+					Length:           1,
+					Version:          sess.version,
+				},
+				PacketNumberLen: protocol.PacketNumberLen1,
+				PacketNumber:    1,
+			}
+			unpacker.EXPECT().Unpack(gomock.Any(), gomock.Any()).Return(nil, handshake.ErrOpenerNotYetAvailable)
+			packet := getPacket(hdr, nil)
+			Expect(sess.handlePacketImpl(packet)).To(BeFalse())
+			Expect(sess.undecryptablePackets).To(Equal([]*receivedPacket{packet}))
+		})
+
 		Context("updating the remote address", func() {
 			It("doesn't support connection migration", func() {
 				unpacker.EXPECT().Unpack(gomock.Any(), gomock.Any()).Return(&unpackedPacket{
@@ -705,6 +724,26 @@ var _ = Describe("Session", func() {
 				Expect(sess.handlePacketImpl(packet1)).To(BeTrue())
 			})
 
+			It("works with undecryptable packets", func() {
+				hdrLen1, packet1 := getPacketWithLength(sess.srcConnID, 456)
+				hdrLen2, packet2 := getPacketWithLength(sess.srcConnID, 123)
+				gomock.InOrder(
+					unpacker.EXPECT().Unpack(gomock.Any(), gomock.Any()).Return(nil, handshake.ErrOpenerNotYetAvailable),
+					unpacker.EXPECT().Unpack(gomock.Any(), gomock.Any()).DoAndReturn(func(_ *wire.Header, data []byte) (*unpackedPacket, error) {
+						Expect(data).To(HaveLen(hdrLen2 + 123 - 3))
+						return &unpackedPacket{
+							encryptionLevel: protocol.EncryptionHandshake,
+							data:            []byte{0},
+						}, nil
+					}),
+				)
+				packet1.data = append(packet1.data, packet2.data...)
+				Expect(sess.handlePacketImpl(packet1)).To(BeTrue())
+
+				Expect(sess.undecryptablePackets).To(HaveLen(1))
+				Expect(sess.undecryptablePackets[0].data).To(HaveLen(hdrLen1 + 456 - 3))
+			})
+
 			It("ignores coalesced packet parts if the destination connection IDs don't match", func() {
 				wrongConnID := protocol.ConnectionID{0xde, 0xad, 0xbe, 0xef}
 				Expect(sess.srcConnID).ToNot(Equal(wrongConnID))