diff --git a/src/connection.c b/src/connection.c
index ad0386352..b970d4189 100644
--- a/src/connection.c
+++ b/src/connection.c
@@ -229,7 +229,7 @@ void conn_fd_handler(int fd)
 	if ((io_available || (((conn->flags ^ flags) & CO_FL_NOTIFY_DATA) ||
 	     ((flags & (CO_FL_CONNECTED|CO_FL_HANDSHAKE)) != CO_FL_CONNECTED &&
 	      (conn->flags & (CO_FL_CONNECTED|CO_FL_HANDSHAKE)) == CO_FL_CONNECTED))) &&
-	    conn->mux->wake(conn) < 0)
+	    conn->mux->wake && conn->mux->wake(conn) < 0)
 		return;
 
 	/* commit polling changes */
diff --git a/src/mux_h2.c b/src/mux_h2.c
index c6fa1c90c..f0df0e0c7 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -222,6 +222,7 @@ static const struct h2s *h2_idle_stream = &(const struct h2s){
 static struct task *h2_timeout_task(struct task *t, void *context, unsigned short state);
 static int h2_send(struct h2c *h2c);
 static int h2_recv(struct h2c *h2c);
+static int h2_process(struct h2c *h2c);
 static struct task *h2_io_cb(struct task *t, void *ctx, unsigned short state);
 static inline struct h2s *h2c_st_by_id(struct h2c *h2c, int id);
 static int h2_frt_decode_headers(struct h2s *h2s);
@@ -282,7 +283,8 @@ static int h2_buf_available(void *target)
 		h2c->flags &= ~H2_CF_DEM_DALLOC;
 		if (h2_recv_allowed(h2c)) {
 			conn_xprt_want_recv(h2c->conn);
-			h2_recv(h2c);
+			if (h2_recv(h2c))
+				h2_process(h2c);
 		}
 		return 1;
 	}
@@ -296,7 +298,8 @@ static int h2_buf_available(void *target)
 			h2c->flags &= ~H2_CF_DEM_MROOM;
 			if (h2_recv_allowed(h2c)) {
 				conn_xprt_want_recv(h2c->conn);
-				h2_recv(h2c);
+				if (h2_recv(h2c))
+					h2_process(h2c);
 			}
 		}
 		return 1;
@@ -308,7 +311,8 @@ static int h2_buf_available(void *target)
 		h2c->flags &= ~H2_CF_DEM_SALLOC;
 		if (h2_recv_allowed(h2c)) {
 			conn_xprt_want_recv(h2c->conn);
-			h2_recv(h2c);
+			if (h2_recv(h2c))
+				h2_process(h2c);
 		}
 		return 1;
 	}
@@ -417,7 +421,8 @@ static int h2c_frt_init(struct connection *conn)
 	LIST_INIT(&h2c->wait_list.list);
 
 	/* Try to read, if nothing is available yet we'll just subscribe */
-	h2_recv(h2c);
+	if (h2_recv(h2c))
+		h2_process(h2c);
 	return 0;
  fail:
 	if (t)
@@ -2239,6 +2244,7 @@ static int h2_recv(struct h2c *h2c)
 	struct connection *conn = h2c->conn;
 	struct buffer *buf;
 	int max;
+	size_t ret;
 
 	if (h2c->wait_list.wait_reason & SUB_CAN_RECV)
 		return 0;
@@ -2252,12 +2258,18 @@ static int h2_recv(struct h2c *h2c)
 		return 0;
 	}
 
-	max = buf->size - b_data(buf);
-	if (max)
-		conn->xprt->rcv_buf(conn, buf, max, 0);
+	do {
+		max = buf->size - b_data(buf);
+		if (max)
+			ret = conn->xprt->rcv_buf(conn, buf, max, 0);
+		else
+			ret = 0;
+	} while (ret > 0);
 
-	if (h2_recv_allowed(h2c))
+	if (h2_recv_allowed(h2c)) {
+		conn_xprt_want_recv(conn);
 		conn->xprt->subscribe(conn, SUB_CAN_RECV, &h2c->wait_list);
+	}
 	if (!b_data(buf)) {
 		h2_release_buf(h2c, &h2c->dbuf);
 		return 0;
@@ -2278,6 +2290,7 @@ static int h2_send(struct h2c *h2c)
 	if (conn->flags & CO_FL_ERROR)
 		return 0;
 
+
 	if (conn->flags & (CO_FL_HANDSHAKE|CO_FL_WAIT_L4_CONN|CO_FL_WAIT_L6_CONN)) {
 		/* a handshake was requested */
 		goto schedule;
@@ -2358,11 +2371,14 @@ schedule:
 static struct task *h2_io_cb(struct task *t, void *ctx, unsigned short status)
 {
 	struct h2c *h2c = ctx;
+	int ret = 0;
 
 	if (!(h2c->wait_list.wait_reason & SUB_CAN_SEND))
-		h2_send(h2c);
+		ret = h2_send(h2c);
 	if (!(h2c->wait_list.wait_reason & SUB_CAN_RECV))
-		h2_recv(h2c);
+		ret |= h2_recv(h2c);
+	if (ret)
+		h2_process(h2c);
 	return NULL;
 }
 
@@ -2370,15 +2386,11 @@ static struct task *h2_io_cb(struct task *t, void *ctx, unsigned short status)
  * It applies changes and returns zero, or < 0 if it wants immediate
  * destruction of the connection (which normally doesn not happen in h2).
  */
-static int h2_wake(struct connection *conn)
+static int h2_process(struct h2c *h2c)
 {
-	struct h2c *h2c = conn->mux_ctx;
+	struct connection *conn = h2c->conn;
 	struct session *sess = conn->owner;
 
-	h2_send(h2c);
-	if (h2_recv_allowed(h2c))
-		h2_recv(h2c);
-
 	if (b_data(&h2c->dbuf) && !(h2c->flags & H2_CF_DEM_BLOCK_ANY)) {
 		h2_process_demux(h2c);
 
@@ -2388,6 +2400,7 @@ static int h2_wake(struct connection *conn)
 		if (!b_full(&h2c->dbuf))
 			h2c->flags &= ~H2_CF_DEM_DFULL;
 	}
+	h2_send(h2c);
 
 	if (sess && unlikely(sess->fe->state == PR_STSTOPPED)) {
 		/* frontend is stopping, reload likely in progress, let's try
@@ -2440,10 +2453,8 @@ static int h2_wake(struct connection *conn)
 	/* stop being notified of incoming data if we can't process them */
 	if (!h2_recv_allowed(h2c))
 		__conn_xprt_stop_recv(conn);
-	else {
+	else
 		__conn_xprt_want_recv(conn);
-		h2_recv(h2c);
-	}
 
 	/* adjust output polling */
 	if (!(conn->flags & CO_FL_SOCK_WR_SH) &&
@@ -2468,6 +2479,7 @@ static int h2_wake(struct connection *conn)
 			h2c->task->expire = TICK_ETERNITY;
 	}
 
+	h2_send(h2c);
 	return 0;
 }
 
@@ -2556,7 +2568,8 @@ static void h2_update_poll(struct conn_stream *cs)
 		h2s->h2c->flags &= ~H2_CF_DEM_SFULL;
 		if (h2s->h2c->dsi == h2s->id) {
 			conn_xprt_want_recv(cs->conn);
-			h2_recv(h2s->h2c);
+			if (h2_recv(h2s->h2c))
+				h2_process(h2s->h2c);
 			conn_xprt_want_send(cs->conn);
 		}
 	}
@@ -2575,6 +2588,7 @@ static void h2_update_poll(struct conn_stream *cs)
 			    !(cs->conn->flags & CO_FL_SOCK_WR_SH))
 				conn_xprt_want_send(cs->conn);
 			LIST_ADDQ(&h2s->h2c->send_list, &h2s->list);
+			tasklet_wakeup(h2s->h2c->wait_list.task);
 		}
 	}
 	else if (!LIST_ISEMPTY(&h2s->list)) {
@@ -3597,8 +3611,11 @@ static size_t h2_snd_buf(struct conn_stream *cs, struct buffer *buf, size_t coun
 	}
 
 	b_del(buf, total);
-	if (total > 0)
+	if (total > 0) {
 		conn_xprt_want_send(h2s->h2c->conn);
+		if (!(h2s->h2c->wait_list.wait_reason & SUB_CAN_SEND))
+			tasklet_wakeup(h2s->h2c->wait_list.task);
+	}
 	return total;
 }
 
@@ -3699,7 +3716,6 @@ static int h2_parse_max_concurrent_streams(char **args, int section_type, struct
 /* The mux operations */
 const struct mux_ops h2_ops = {
 	.init = h2_init,
-	.wake = h2_wake,
 	.update_poll = h2_update_poll,
 	.snd_buf = h2_snd_buf,
 	.rcv_buf = h2_rcv_buf,