diff --git a/go.mod b/go.mod
index 2281a15..16c65c6 100644
--- a/go.mod
+++ b/go.mod
@@ -3,7 +3,7 @@ module github.com/marten-seemann/webtransport-go
 go 1.17
 
 require (
-	github.com/lucas-clemente/quic-go v0.27.1-0.20220520111257-8185d1b4e072
+	github.com/lucas-clemente/quic-go v0.27.1-0.20220526175250-9d5de12933f2
 	github.com/stretchr/testify v1.7.1
 )
 
diff --git a/go.sum b/go.sum
index 19ca405..f349cc4 100644
--- a/go.sum
+++ b/go.sum
@@ -75,8 +75,8 @@ github.com/kr/pty v1.1.1/go.mod h1:pFQYn66WHrOpPYNljwOMqo10TkYh1fy3cYio2l3bCsQ=
 github.com/kr/pty v1.1.3/go.mod h1:pFQYn66WHrOpPYNljwOMqo10TkYh1fy3cYio2l3bCsQ=
 github.com/kr/text v0.1.0 h1:45sCR5RtlFHMR4UwH9sdQ5TC8v0qDQCHnXt+kaKSTVE=
 github.com/kr/text v0.1.0/go.mod h1:4Jbv+DJW3UT/LiOwJeYQe1efqtUx/iVham/4vfdArNI=
-github.com/lucas-clemente/quic-go v0.27.1-0.20220520111257-8185d1b4e072 h1:s2A290bfKQCyFrBjpWti5klxhHgWOLfyV8LX3PfeVBM=
-github.com/lucas-clemente/quic-go v0.27.1-0.20220520111257-8185d1b4e072/go.mod h1:AzgQoPda7N+3IqMMMkywBKggIFo2KT6pfnlrQ2QieeI=
+github.com/lucas-clemente/quic-go v0.27.1-0.20220526175250-9d5de12933f2 h1:qUX8EnM3HZ03HK3NFZx7pd6zCuUsQjA+VW8gO5vtbEQ=
+github.com/lucas-clemente/quic-go v0.27.1-0.20220526175250-9d5de12933f2/go.mod h1:AzgQoPda7N+3IqMMMkywBKggIFo2KT6pfnlrQ2QieeI=
 github.com/lunixbochs/vtclean v1.0.0/go.mod h1:pHhQNgMf3btfWnGBVipUOjRYhoOsdGqdm/+2c2E2WMI=
 github.com/mailru/easyjson v0.0.0-20190312143242-1de009706dbe/go.mod h1:C1wdFJiN94OJF2b5HbByQZoLdCWB1Yqtg26g4irojpc=
 github.com/marten-seemann/qpack v0.2.1 h1:jvTsT/HpCn2UZJdP+UUB53FfUUgeOyG5K1ns0OJOGVs=
diff --git a/stream.go b/stream.go
index 33b9e93..3a011da 100644
--- a/stream.go
+++ b/stream.go
@@ -46,12 +46,20 @@ func newSendStream(str quic.SendStream, hdr []byte) SendStream {
 	return &sendStream{str: str, streamHdr: hdr}
 }
 
+func (s *sendStream) maybeSendStreamHeader() error {
+	if len(s.streamHdr) == 0 {
+		return nil
+	}
+	if _, err := s.str.Write(s.streamHdr); err != nil {
+		return err
+	}
+	s.streamHdr = nil
+	return nil
+}
+
 func (s *sendStream) Write(b []byte) (int, error) {
-	if len(s.streamHdr) > 0 {
-		if _, err := s.str.Write(s.streamHdr); err != nil {
-			return 0, err
-		}
-		s.streamHdr = nil
+	if err := s.maybeSendStreamHeader(); err != nil {
+		return 0, err
 	}
 	n, err := s.str.Write(b)
 	return n, maybeConvertStreamError(err)
@@ -62,6 +70,9 @@ func (s *sendStream) CancelWrite(e ErrorCode) {
 }
 
 func (s *sendStream) Close() error {
+	if err := s.maybeSendStreamHeader(); err != nil {
+		return err
+	}
 	return maybeConvertStreamError(s.str.Close())
 }
 
diff --git a/webtransport_test.go b/webtransport_test.go
index 5e973e5..3aa7e9e 100644
--- a/webtransport_test.go
+++ b/webtransport_test.go
@@ -109,7 +109,7 @@ func getRandomData(l int) []byte {
 	return data
 }
 
-func TestBidirectionalStreams(t *testing.T) {
+func TestBidirectionalStreamsDataTransfer(t *testing.T) {
 	t.Run("client-initiated", func(t *testing.T) {
 		conn, closeServer := establishConn(t, newEchoHandler(t))
 		defer closeServer()
@@ -130,6 +130,89 @@ func TestBidirectionalStreams(t *testing.T) {
 	})
 }
 
+func TestBidirectionalStreamsImmediateClose(t *testing.T) {
+	t.Run("bidirectional streams", func(t *testing.T) {
+		t.Run("client-initiated", func(t *testing.T) {
+			conn, closeServer := establishConn(t, func(c *webtransport.Conn) {
+				str, err := c.AcceptStream(context.Background())
+				require.NoError(t, err)
+				n, err := str.Read([]byte{0})
+				require.Zero(t, n)
+				require.ErrorIs(t, err, io.EOF)
+				require.NoError(t, str.Close())
+			})
+			defer closeServer()
+
+			str, err := conn.OpenStream()
+			require.NoError(t, err)
+			require.NoError(t, str.Close())
+			n, err := str.Read([]byte{0})
+			require.Zero(t, n)
+			require.ErrorIs(t, err, io.EOF)
+		})
+
+		t.Run("server-initiated", func(t *testing.T) {
+			done := make(chan struct{})
+			conn, closeServer := establishConn(t, func(c *webtransport.Conn) {
+				defer close(done)
+				str, err := c.OpenStream()
+				require.NoError(t, err)
+				require.NoError(t, str.Close())
+				n, err := str.Read([]byte{0})
+				require.Zero(t, n)
+				require.ErrorIs(t, err, io.EOF)
+			})
+			defer closeServer()
+
+			str, err := conn.AcceptStream(context.Background())
+			require.NoError(t, err)
+			n, err := str.Read([]byte{0})
+			require.Zero(t, n)
+			require.ErrorIs(t, err, io.EOF)
+			require.NoError(t, str.Close())
+			<-done
+		})
+	})
+
+	t.Run("unidirectional", func(t *testing.T) {
+		t.Run("client-initiated", func(t *testing.T) {
+			done := make(chan struct{})
+			conn, closeServer := establishConn(t, func(c *webtransport.Conn) {
+				defer close(done)
+				str, err := c.AcceptUniStream(context.Background())
+				require.NoError(t, err)
+				n, err := str.Read([]byte{0})
+				require.Zero(t, n)
+				require.ErrorIs(t, err, io.EOF)
+			})
+			defer closeServer()
+
+			str, err := conn.OpenUniStream()
+			require.NoError(t, err)
+			require.NoError(t, str.Close())
+			<-done
+		})
+
+		t.Run("server-initiated", func(t *testing.T) {
+			done := make(chan struct{})
+			conn, closeServer := establishConn(t, func(c *webtransport.Conn) {
+				defer close(done)
+				str, err := c.OpenUniStream()
+				require.NoError(t, err)
+				require.NoError(t, str.Close())
+			})
+			defer closeServer()
+
+			str, err := conn.AcceptUniStream(context.Background())
+			require.NoError(t, err)
+			n, err := str.Read([]byte{0})
+			require.Zero(t, n)
+			require.ErrorIs(t, err, io.EOF)
+			<-done
+		})
+	})
+}
+
 func TestUnidirectionalStreams(t *testing.T) {
 	conn, closeServer := establishConn(t, func(conn *webtransport.Conn) {
 		// Accept a unidirectional stream, read all of its contents,