diff --git a/include/types/connection.h b/include/types/connection.h
index 13cbf73..624e01e 100644
--- a/include/types/connection.h
+++ b/include/types/connection.h
@@ -243,7 +243,12 @@
 	CO_SRC_BIND        = 0x0008,    /* bind to a specific source address when connecting */
 };
 
-/* flags that can be passed to xprt->snd_buf() */
+/* flags that can be passed to xprt->rcv_buf() and mux->rcv_buf() */
+enum {
+	CO_RFL_BUF_WET     = 0x0001,    /* Buffer still has some output data present */
+};
+
+/* flags that can be passed to xprt->snd_buf() and mux->snd_buf() */
 enum {
 	CO_SFL_MSG_MORE    = 0x0001,    /* More data to come afterwards */
 	CO_SFL_STREAMER    = 0x0002,    /* Producer is continuously streaming data */
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 250eae2..207589b 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2614,7 +2614,7 @@
  * proceed. Stream errors are reported in h2s->errcode and connection errors
  * in h2c->errcode.
  */
-static int h2_frt_decode_headers(struct h2s *h2s, struct buffer *buf, int count)
+static int h2_frt_decode_headers(struct h2s *h2s, struct buffer *buf, int count, int flags)
 {
 	struct h2c *h2c = h2s->h2c;
 	const uint8_t *hdrs = (uint8_t *)h2c->dbuf->p;
@@ -2689,7 +2689,7 @@
 	 * always empty except maybe for trailers, so these operations almost
 	 * never happen.
 	 */
-	if (unlikely(buf->o)) {
+	if (flags & CO_RFL_BUF_WET) {
 		/* need to let the output buffer flush and
 		 * mark the buffer for later wake up.
 		 */
@@ -2775,7 +2775,7 @@
  * frame header and ensured that the frame was complete or the buffer full. It
  * changes the frame state to FRAME_A once done.
  */
-static int h2_frt_transfer_data(struct h2s *h2s, struct buffer *buf, int count)
+static int h2_frt_transfer_data(struct h2s *h2s, struct buffer *buf, int count, int flags)
 {
 	struct h2c *h2c = h2s->h2c;
 	int block1, block2;
@@ -2937,11 +2937,11 @@
 
 	switch (h2c->dft) {
 	case H2_FT_HEADERS:
-		ret = h2_frt_decode_headers(h2s, buf, count);
+		ret = h2_frt_decode_headers(h2s, buf, count, flags);
 		break;
 
 	case H2_FT_DATA:
-		ret = h2_frt_transfer_data(h2s, buf, count);
+		ret = h2_frt_transfer_data(h2s, buf, count, flags);
 		break;
 
 	default:
diff --git a/src/stream_interface.c b/src/stream_interface.c
index 0afcb97..2677b2f 100644
--- a/src/stream_interface.c
+++ b/src/stream_interface.c
@@ -1189,7 +1189,7 @@
 			break;
 		}
 
-		ret = conn->mux->rcv_buf(cs, ic->buf, max, 0);
+		ret = conn->mux->rcv_buf(cs, ic->buf, max, co_data(ic) ? CO_RFL_BUF_WET : 0);
 		if (cs->flags & CS_FL_RCV_MORE)
 			si->flags |= SI_FL_WAIT_ROOM;