diff --git a/http2/writesched.go b/http2/writesched.go
index f24d2b1e7..c7cd00173 100644
--- a/http2/writesched.go
+++ b/http2/writesched.go
@@ -32,7 +32,8 @@ type WriteScheduler interface {
 
 	// Pop dequeues the next frame to write. Returns false if no frames can
 	// be written. Frames with a given wr.StreamID() are Pop'd in the same
-	// order they are Push'd. No frames should be discarded except by CloseStream.
+	// order they are Push'd, except RST_STREAM frames. No frames should be
+	// discarded except by CloseStream.
 	Pop() (wr FrameWriteRequest, ok bool)
 }
 
@@ -52,6 +53,7 @@ type FrameWriteRequest struct {
 
 	// stream is the stream on which this frame will be written.
 	// nil for non-stream frames like PING and SETTINGS.
+	// nil for RST_STREAM streams, which use the StreamError.StreamID field instead.
 	stream *stream
 
 	// done, if non-nil, must be a buffered channel with space for
diff --git a/http2/writesched_random.go b/http2/writesched_random.go
index 9a7b9e581..f2e55e05c 100644
--- a/http2/writesched_random.go
+++ b/http2/writesched_random.go
@@ -45,11 +45,11 @@ func (ws *randomWriteScheduler) AdjustStream(streamID uint32, priority PriorityP
 }
 
 func (ws *randomWriteScheduler) Push(wr FrameWriteRequest) {
-	id := wr.StreamID()
-	if id == 0 {
+	if wr.isControl() {
 		ws.zero.push(wr)
 		return
 	}
+	id := wr.StreamID()
 	q, ok := ws.sq[id]
 	if !ok {
 		q = ws.queuePool.get()
@@ -59,7 +59,7 @@ func (ws *randomWriteScheduler) Push(wr FrameWriteRequest) {
 }
 
 func (ws *randomWriteScheduler) Pop() (FrameWriteRequest, bool) {
-	// Control frames first.
+	// Control and RST_STREAM frames first.
 	if !ws.zero.empty() {
 		return ws.zero.shift(), true
 	}
diff --git a/http2/writesched_random_test.go b/http2/writesched_random_test.go
index 1f501b4bd..02a41f36b 100644
--- a/http2/writesched_random_test.go
+++ b/http2/writesched_random_test.go
@@ -14,8 +14,9 @@ func TestRandomScheduler(t *testing.T) {
 	ws.Push(makeWriteHeadersRequest(2))
 	ws.Push(makeWriteNonStreamRequest())
 	ws.Push(makeWriteNonStreamRequest())
+	ws.Push(makeWriteRSTStream(1))
 
-	// Pop all frames. Should get the non-stream requests first,
+	// Pop all frames. Should get the non-stream and RST stream requests first,
 	// followed by the stream requests in any order.
 	var order []FrameWriteRequest
 	for {
@@ -26,12 +27,15 @@ func TestRandomScheduler(t *testing.T) {
 		order = append(order, wr)
 	}
 	t.Logf("got frames: %v", order)
-	if len(order) != 6 {
+	if len(order) != 7 {
 		t.Fatalf("got %d frames, expected 6", len(order))
 	}
 	if order[0].StreamID() != 0 || order[1].StreamID() != 0 {
 		t.Fatal("expected non-stream frames first", order[0], order[1])
 	}
+	if _, ok := order[2].write.(StreamError); !ok {
+		t.Fatal("expected RST stream frames first", order[2])
+	}
 	got := make(map[uint32]bool)
 	for _, wr := range order[2:] {
 		got[wr.StreamID()] = true
diff --git a/http2/writesched_test.go b/http2/writesched_test.go
index 99be5a771..6dbd7f0ad 100644
--- a/http2/writesched_test.go
+++ b/http2/writesched_test.go
@@ -25,6 +25,10 @@ func makeHandlerPanicRST(streamID uint32) FrameWriteRequest {
 	return FrameWriteRequest{&handlerPanicRST{StreamID: streamID}, st, nil}
 }
 
+func makeWriteRSTStream(streamID uint32) FrameWriteRequest {
+	return FrameWriteRequest{write: streamError(streamID, ErrCodeInternal)}
+}
+
 func checkConsume(wr FrameWriteRequest, nbytes int32, want []FrameWriteRequest) error {
 	consumed, rest, n := wr.Consume(nbytes)
 	var wantConsumed, wantRest FrameWriteRequest
@@ -52,6 +56,56 @@ func TestFrameWriteRequestNonData(t *testing.T) {
 	if err := checkConsume(wr, 0, []FrameWriteRequest{wr}); err != nil {
 		t.Errorf("Consume:\n%v", err)
 	}
+
+	wr = makeWriteRSTStream(123)
+	if got, want := wr.DataSize(), 0; got != want {
+		t.Errorf("DataSize: got %v, want %v", got, want)
+	}
+
+	// RST_STREAM frames are always consumed whole.
+	if err := checkConsume(wr, 0, []FrameWriteRequest{wr}); err != nil {
+		t.Errorf("Consume:\n%v", err)
+	}
+}
+
+// #49741 RST_STREAM and Control frames should have more priority than data
+// frames to avoid blocking streams caused by clients not able to drain the
+// queue.
+func TestFrameWriteRequestWithData(t *testing.T) {
+	st := &stream{
+		id: 1,
+		sc: &serverConn{maxFrameSize: 16},
+	}
+	const size = 32
+	wr := FrameWriteRequest{&writeData{st.id, make([]byte, size), true}, st, make(chan error)}
+	if got, want := wr.DataSize(), size; got != want {
+		t.Errorf("DataSize: got %v, want %v", got, want)
+	}
+
+	// No flow-control bytes available: cannot consume anything.
+	if err := checkConsume(wr, math.MaxInt32, []FrameWriteRequest{}); err != nil {
+		t.Errorf("Consume(limited by flow control):\n%v", err)
+	}
+
+	wr = makeWriteNonStreamRequest()
+	if got, want := wr.DataSize(), 0; got != want {
+		t.Errorf("DataSize: got %v, want %v", got, want)
+	}
+
+	// Non-DATA frames are always consumed whole.
+	if err := checkConsume(wr, 0, []FrameWriteRequest{wr}); err != nil {
+		t.Errorf("Consume:\n%v", err)
+	}
+
+	wr = makeWriteRSTStream(1)
+	if got, want := wr.DataSize(), 0; got != want {
+		t.Errorf("DataSize: got %v, want %v", got, want)
+	}
+
+	// RST_STREAM frames are always consumed whole.
+	if err := checkConsume(wr, 0, []FrameWriteRequest{wr}); err != nil {
+		t.Errorf("Consume:\n%v", err)
+	}
 }
 
 func TestFrameWriteRequestData(t *testing.T) {