diff --git a/send_stream.go b/send_stream.go
index bbc5140e..1a09eec9 100644
--- a/send_stream.go
+++ b/send_stream.go
@@ -398,7 +398,7 @@ func (s *sendStream) isNewlyCompleted() bool {
 
 func (s *sendStream) Close() error {
 	s.mutex.Lock()
-	if s.closeForShutdownErr != nil {
+	if s.closeForShutdownErr != nil || s.finishedWriting {
 		s.mutex.Unlock()
 		return nil
 	}
diff --git a/send_stream_test.go b/send_stream_test.go
index 7859820a..a5638c07 100644
--- a/send_stream_test.go
+++ b/send_stream_test.go
@@ -431,8 +431,6 @@ func TestSendStreamClose(t *testing.T) {
 	require.False(t, hasMore)
 
 	// further calls to Close don't do anything
-	// TODO(#4800): there shouldn't be any calls to mockSender
-	mockSender.EXPECT().onHasStreamData(streamID, str)
 	require.NoError(t, str.Close())
 	_, ok, hasMore = str.popStreamFrame(protocol.MaxByteCount, protocol.Version1)
 	require.False(t, ok)