diff --git a/include/types/connection.h b/include/types/connection.h
index a85343bdd..5af651ff5 100644
--- a/include/types/connection.h
+++ b/include/types/connection.h
@@ -258,6 +258,7 @@ enum {
 /* 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 */
+	CO_RFL_BUF_FLUSH   = 0x0002,    /* Flush mux's buffers but don't read more data */
 };
 
 /* flags that can be passed to xprt->snd_buf() and mux->snd_buf() */
diff --git a/src/stream_interface.c b/src/stream_interface.c
index 22c329fc1..8742a400f 100644
--- a/src/stream_interface.c
+++ b/src/stream_interface.c
@@ -1090,6 +1090,7 @@ int si_cs_recv(struct conn_stream *cs)
 	struct channel *ic = si_ic(si);
 	int ret, max, cur_read = 0;
 	int read_poll = MAX_READ_POLL_LOOPS;
+	int flags = 0;
 
 	/* stop immediately on errors. Note that we DON'T want to stop on
 	 * POLL_ERR, as the poller might report a write error while there
@@ -1141,6 +1142,7 @@ int si_cs_recv(struct conn_stream *cs)
 			 * locations at a time. Let's indicate we need some
 			 * place and ask the consumer to hurry.
 			 */
+			flags |= CO_RFL_BUF_FLUSH;
 			goto abort_splice;
 		}
 
@@ -1208,8 +1210,7 @@ int si_cs_recv(struct conn_stream *cs)
 		 * CS_FL_RCV_MORE on the CS if more space is needed.
 		 */
 		max = channel_recv_max(ic);
-
-		ret = cs->conn->mux->rcv_buf(cs, &ic->buf, max, co_data(ic) ? CO_RFL_BUF_WET : 0);
+		ret = cs->conn->mux->rcv_buf(cs, &ic->buf, max, flags | (co_data(ic) ? CO_RFL_BUF_WET : 0));
 		if (cs->flags & CS_FL_RCV_MORE)
 			si_rx_room_blk(si);