diff --git a/src/stream.c b/src/stream.c
index 8e115e595..fe07d4de5 100644
--- a/src/stream.c
+++ b/src/stream.c
@@ -673,6 +673,7 @@ static int sess_update_st_con_tcp(struct stream *s)
 	/* OK, this means that a connection succeeded. The caller will be
 	 * responsible for handling the transition from CON to EST.
 	 */
+	si_want_put(si);
 	si->state    = SI_ST_EST;
 	si->err_type = SI_ET_NONE;
 	return 1;
diff --git a/src/stream_interface.c b/src/stream_interface.c
index 65d2c6120..1999589b8 100644
--- a/src/stream_interface.c
+++ b/src/stream_interface.c
@@ -475,12 +475,13 @@ void stream_int_notify(struct stream_interface *si)
 		if (!(si->flags & SI_FL_INDEP_STR))
 			if (tick_isset(ic->rex))
 				ic->rex = tick_add_ifset(now_ms, ic->rto);
+	}
 
-		if (likely((oc->flags & (CF_SHUTW|CF_WRITE_PARTIAL|CF_DONT_READ)) == CF_WRITE_PARTIAL &&
-		           (si_opposite(si)->flags & SI_FL_WAIT_ROOM))) {
-			si_opposite(si)->flags &= ~SI_FL_WAIT_ROOM;
-			si_chk_rcv(si_opposite(si));
-		}
+	if ((si_opposite(si)->flags & SI_FL_WAIT_ROOM) &&
+	    ((oc->flags & (CF_SHUTW|CF_WRITE_PARTIAL|CF_DONT_READ)) == CF_WRITE_PARTIAL ||
+	     channel_is_empty(oc))) {
+		si_opposite(si)->flags &= ~SI_FL_WAIT_ROOM;
+		si_chk_rcv(si_opposite(si));
 	}
 
 	/* Notify the other side when we've injected data into the IC that
@@ -745,13 +746,10 @@ void stream_int_update(struct stream_interface *si)
 	struct channel *oc = si_oc(si);
 
 	if (!(ic->flags & CF_SHUTR)) {
-		if (!(ic->flags & CF_DONT_READ))
-			si_want_put(si);
-
 		/* Read not closed, update FD status and timeout for reads */
 		if ((ic->flags & CF_DONT_READ) || co_data(ic)) {
-			/* stop reading */
-			si_stop_put(si);
+			/* stop reading, imposed by channel's policy or contents */
+			si_cant_put(si);
 			ic->rex = TICK_ETERNITY;
 		}
 		else {
@@ -846,14 +844,7 @@ void si_update_both(struct stream_interface *si_f, struct stream_interface *si_b
 	}
 
 	/* it's time to try to receive */
-	if (!(req->flags & (CF_SHUTR|CF_DONT_READ)))
-		si_want_put(si_f);
-
 	si_chk_rcv(si_f);
-
-	if (!(res->flags & (CF_SHUTR|CF_DONT_READ)))
-		si_want_put(si_b);
-
 	si_chk_rcv(si_b);
 
 	/* let's recompute both sides states */
@@ -1133,9 +1124,6 @@ int si_cs_recv(struct conn_stream *cs)
 	if (si->wait_event.wait_reason & SUB_CAN_RECV)
 		return 0;
 
-	/* by default nothing to deliver */
-	si_stop_put(si);
-
 	/* maybe we were called immediately after an asynchronous shutr */
 	if (ic->flags & CF_SHUTR)
 		return 1;
@@ -1144,6 +1132,9 @@ int si_cs_recv(struct conn_stream *cs)
 	if (cs->flags & CS_FL_EOS)
 		goto out_shutdown_r;
 
+	/* start by claiming we'll want to receive and change our mind later if needed */
+	si_want_put(si);
+
 	if ((ic->flags & (CF_STREAMER | CF_STREAMER_FAST)) && !co_data(ic) &&
 	    global.tune.idle_timer &&
 	    (unsigned short)(now_ms - ic->last_read) >= global.tune.idle_timer) {
@@ -1235,8 +1226,10 @@ int si_cs_recv(struct conn_stream *cs)
 		if (cs->flags & CS_FL_RCV_MORE)
 			si_cant_put(si);
 
-		if (ret <= 0)
+		if (ret <= 0) {
+			si_stop_put(si);
 			break;
+		}
 
 		cur_read += ret;
 
@@ -1254,8 +1247,11 @@ int si_cs_recv(struct conn_stream *cs)
 		ic->flags |= CF_READ_PARTIAL;
 		ic->total += ret;
 
-		if ((ic->flags & CF_READ_DONTWAIT) || --read_poll <= 0)
+		if ((ic->flags & CF_READ_DONTWAIT) || --read_poll <= 0) {
+			/* we're stopped by the channel's policy */
+			si_cant_put(si);
 			break;
+		}
 
 		/* if too many bytes were missing from last read, it means that
 		 * it's pointless trying to read again because the system does
@@ -1266,14 +1262,20 @@ int si_cs_recv(struct conn_stream *cs)
 			 * have exhausted system buffers. It's not worth trying
 			 * again.
 			 */
-			if (ic->flags & CF_STREAMER)
+			if (ic->flags & CF_STREAMER) {
+				/* we're stopped by the channel's policy */
+				si_cant_put(si);
 				break;
+			}
 
 			/* if we read a large block smaller than what we requested,
 			 * it's almost certain we'll never get anything more.
 			 */
-			if (ret >= global.tune.recv_enough)
+			if (ret >= global.tune.recv_enough) {
+				/* we're stopped by the channel's policy */
+				si_cant_put(si);
 				break;
+			}
 		}
 
 		/* if we are waiting for more space, don't try to read more data