diff --git a/src/mux_h2.c b/src/mux_h2.c
index 08cc574ef..f05c26939 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -938,6 +938,36 @@ static struct conn_stream *h2_attach(struct connection *conn)
  */
 static void h2_update_poll(struct conn_stream *cs)
 {
+	struct h2s *h2s = cs->ctx;
+
+	if (!h2s)
+		return;
+
+	/* Note: the stream and stream-int code doesn't allow us to perform a
+	 * synchronous send() here unfortunately, because this code is called
+	 * as si_update() from the process_stream() context. This means that
+	 * we have to queue the current cs and defer its processing after the
+	 * connection's cs list is processed anyway.
+	 */
+
+	if (cs->flags & CS_FL_DATA_WR_ENA) {
+		if (LIST_ISEMPTY(&h2s->list)) {
+			if (LIST_ISEMPTY(&h2s->h2c->send_list) &&
+			    !h2s->h2c->mbuf->o && // not yet subscribed
+			    !(cs->conn->flags & CO_FL_SOCK_WR_SH))
+				conn_xprt_want_send(cs->conn);
+			LIST_ADDQ(&h2s->h2c->send_list, &h2s->list);
+		}
+	}
+	else if (!LIST_ISEMPTY(&h2s->list)) {
+		LIST_DEL(&h2s->list);
+		LIST_INIT(&h2s->list);
+		h2s->flags &= ~(H2_SF_BLK_MBUSY | H2_SF_BLK_MROOM | H2_SF_BLK_MFCTL);
+	}
+
+	/* this can happen from within si_chk_snd() */
+	if (h2s->h2c->mbuf->o && !(cs->conn->flags & CO_FL_XPRT_WR_ENA))
+		conn_xprt_want_send(cs->conn);
 }
 
 /*