diff --git a/connection.go b/connection.go
index b17f3ce81a3..877f2d03311 100644
--- a/connection.go
+++ b/connection.go
@@ -243,7 +243,7 @@ var newConnection = func(
 		handshakeDestConnID: destConnID,
 		srcConnIDLen:        srcConnID.Len(),
 		tokenGenerator:      tokenGenerator,
-		oneRTTStream:        newCryptoStream(),
+		oneRTTStream:        newCryptoStream(true),
 		perspective:         protocol.PerspectiveServer,
 		tracer:              tracer,
 		logger:              logger,
@@ -391,7 +391,7 @@ var newClientConnection = func(
 		s.logger,
 	)
 	s.mtuDiscoverer = newMTUDiscoverer(s.rttStats, getMaxPacketSize(s.conn.RemoteAddr()), s.sentPacketHandler.SetMaxDatagramSize)
-	oneRTTStream := newCryptoStream()
+	oneRTTStream := newCryptoStream(true)
 	params := &wire.TransportParameters{
 		InitialMaxStreamDataBidiRemote: protocol.ByteCount(s.config.InitialStreamReceiveWindow),
 		InitialMaxStreamDataBidiLocal:  protocol.ByteCount(s.config.InitialStreamReceiveWindow),
@@ -447,8 +447,8 @@ var newClientConnection = func(
 }
 
 func (s *connection) preSetup() {
-	s.initialStream = newCryptoStream()
-	s.handshakeStream = newCryptoStream()
+	s.initialStream = newCryptoStream(false)
+	s.handshakeStream = newCryptoStream(false)
 	s.sendQueue = newSendQueue(s.conn)
 	s.retransmissionQueue = newRetransmissionQueue()
 	s.frameParser = wire.NewFrameParser(s.config.EnableDatagrams)
diff --git a/crypto_stream.go b/crypto_stream.go
index 4be2a07ae1a..5ce2125decf 100644
--- a/crypto_stream.go
+++ b/crypto_stream.go
@@ -30,10 +30,17 @@ type cryptoStreamImpl struct {
 
 	writeOffset protocol.ByteCount
 	writeBuf    []byte
+
+	// Reassemble TLS handshake messages before returning them from GetCryptoData.
+	// This is only needed because crypto/tls doesn't correctly handle post-handshake messages.
+	onlyCompleteMsg bool
 }
 
-func newCryptoStream() cryptoStream {
-	return &cryptoStreamImpl{queue: newFrameSorter()}
+func newCryptoStream(onlyCompleteMsg bool) cryptoStream {
+	return &cryptoStreamImpl{
+		queue:           newFrameSorter(),
+		onlyCompleteMsg: onlyCompleteMsg,
+	}
 }
 
 func (s *cryptoStreamImpl) HandleCryptoFrame(f *wire.CryptoFrame) error {
@@ -71,6 +78,20 @@ func (s *cryptoStreamImpl) HandleCryptoFrame(f *wire.CryptoFrame) error {
 
 // GetCryptoData retrieves data that was received in CRYPTO frames
 func (s *cryptoStreamImpl) GetCryptoData() []byte {
+	if s.onlyCompleteMsg {
+		if len(s.msgBuf) < 4 {
+			return nil
+		}
+		msgLen := 4 + int(s.msgBuf[1])<<16 + int(s.msgBuf[2])<<8 + int(s.msgBuf[3])
+		if len(s.msgBuf) < msgLen {
+			return nil
+		}
+		msg := make([]byte, msgLen)
+		copy(msg, s.msgBuf[:msgLen])
+		s.msgBuf = s.msgBuf[msgLen:]
+		return msg
+	}
+
 	b := s.msgBuf
 	s.msgBuf = nil
 	return b
diff --git a/crypto_stream_test.go b/crypto_stream_test.go
index 9a4a2ee57f9..67de9149966 100644
--- a/crypto_stream_test.go
+++ b/crypto_stream_test.go
@@ -1,6 +1,7 @@
 package quic
 
 import (
+	"crypto/rand"
 	"fmt"
 
 	"github.com/quic-go/quic-go/internal/protocol"
@@ -15,7 +16,7 @@ var _ = Describe("Crypto Stream", func() {
 	var str cryptoStream
 
 	BeforeEach(func() {
-		str = newCryptoStream()
+		str = newCryptoStream(false)
 	})
 
 	Context("handling incoming data", func() {
@@ -137,4 +138,23 @@ var _ = Describe("Crypto Stream", func() {
 			Expect(f.Data).To(Equal([]byte("bar")))
 		})
 	})
+
+	It("reassembles data", func() {
+		str = newCryptoStream(true)
+		data := make([]byte, 1337)
+		l := len(data) - 4
+		data[1] = uint8(l >> 16)
+		data[2] = uint8(l >> 8)
+		data[3] = uint8(l)
+		rand.Read(data[4:])
+
+		for i, b := range data {
+			Expect(str.GetCryptoData()).To(BeEmpty())
+			Expect(str.HandleCryptoFrame(&wire.CryptoFrame{
+				Offset: protocol.ByteCount(i),
+				Data:   []byte{b},
+			})).To(Succeed())
+		}
+		Expect(str.GetCryptoData()).To(Equal(data))
+	})
 })
diff --git a/fuzzing/handshake/fuzz.go b/fuzzing/handshake/fuzz.go
index a3f549eec7f..be34c22da9e 100644
--- a/fuzzing/handshake/fuzz.go
+++ b/fuzzing/handshake/fuzz.go
@@ -408,6 +408,7 @@ func runHandshake(runConfig [confLen]byte, messageConfig uint8, clientConf *tls.
 		}
 		client.HandleMessage(ticket, protocol.Encryption1RTT)
 	}
+
 	if sendPostHandshakeMessageToClient {
 		fmt.Println("sending post handshake message to the client at", messageToReplaceEncLevel)
 		client.HandleMessage(data, messageToReplaceEncLevel)