diff --git a/include/proto/stream.h b/include/proto/stream.h
index 5ff22916a..44fc8bea5 100644
--- a/include/proto/stream.h
+++ b/include/proto/stream.h
@@ -35,7 +35,7 @@ extern struct list streams;
 
 extern struct data_cb sess_conn_cb;
 
-struct stream *stream_new(struct session *sess, struct task *t, enum obj_type *origin);
+struct stream *stream_new(struct session *sess, enum obj_type *origin);
 
 /* perform minimal intializations, report 0 in case of error, 1 if OK. */
 int init_stream();
diff --git a/src/flt_spoe.c b/src/flt_spoe.c
index 1a8bd2c0f..47aef5762 100644
--- a/src/flt_spoe.c
+++ b/src/flt_spoe.c
@@ -1901,7 +1901,6 @@ spoe_create_appctx(struct spoe_config *conf)
 {
 	struct appctx      *appctx;
 	struct session     *sess;
-	struct task        *task;
 	struct stream      *strm;
 
 	if ((appctx = appctx_new(&spoe_applet)) == NULL)
@@ -1937,12 +1936,9 @@ spoe_create_appctx(struct spoe_config *conf)
 	if (!sess)
 		goto out_free_spoe;
 
-	if ((task = task_new()) == NULL)
+	if ((strm = stream_new(sess, &appctx->obj_type)) == NULL)
 		goto out_free_sess;
 
-	if ((strm = stream_new(sess, task, &appctx->obj_type)) == NULL)
-		goto out_free_task;
-
 	stream_set_backend(strm, conf->agent->b.be);
 
 	/* applet is waiting for data */
@@ -1960,12 +1956,10 @@ spoe_create_appctx(struct spoe_config *conf)
 	LIST_ADDQ(&conf->agent->applets, &SPOE_APPCTX(appctx)->list);
 	conf->agent->applets_act++;
 
-	task_wakeup(task, TASK_WOKEN_INIT);
+	task_wakeup(strm->task, TASK_WOKEN_INIT);
 	return appctx;
 
 	/* Error unrolling */
- out_free_task:
-	task_free(task);
  out_free_sess:
 	session_free(sess);
  out_free_spoe:
diff --git a/src/hlua.c b/src/hlua.c
index 0f82425de..594d880ed 100644
--- a/src/hlua.c
+++ b/src/hlua.c
@@ -2297,7 +2297,6 @@ __LJMP static int hlua_socket_new(lua_State *L)
 	struct appctx *appctx;
 	struct session *sess;
 	struct stream *strm;
-	struct task *task;
 
 	/* Check stack size. */
 	if (!lua_checkstack(L, 3)) {
@@ -2341,14 +2340,7 @@ __LJMP static int hlua_socket_new(lua_State *L)
 		goto out_fail_sess;
 	}
 
-	task = task_new();
-	if (!task) {
-		hlua_pusherror(L, "socket: out of memory");
-		goto out_fail_task;
-	}
-	task->nice = 0;
-
-	strm = stream_new(sess, task, &appctx->obj_type);
+	strm = stream_new(sess, &appctx->obj_type);
 	if (!strm) {
 		hlua_pusherror(L, "socket: out of memory");
 		goto out_fail_stream;
@@ -2372,13 +2364,11 @@ __LJMP static int hlua_socket_new(lua_State *L)
 	jobs++;
 	totalconn++;
 
-	task_wakeup(task, TASK_WOKEN_INIT);
+	task_wakeup(strm->task, TASK_WOKEN_INIT);
 	/* Return yield waiting for connection. */
 	return 1;
 
  out_fail_stream:
-	task_free(task);
- out_fail_task:
 	session_free(sess);
  out_fail_sess:
 	appctx_free(appctx);
diff --git a/src/peers.c b/src/peers.c
index 249edf7a3..d03e72fef 100644
--- a/src/peers.c
+++ b/src/peers.c
@@ -1784,7 +1784,6 @@ static struct appctx *peer_session_create(struct peers *peers, struct peer *peer
 	struct appctx *appctx;
 	struct session *sess;
 	struct stream *s;
-	struct task *t;
 	struct connection *conn;
 
 	peer->reconnect = tick_add(now_ms, MS_TO_TICKS(5000));
@@ -1804,15 +1803,9 @@ static struct appctx *peer_session_create(struct peers *peers, struct peer *peer
 		goto out_free_appctx;
 	}
 
-	if ((t = task_new()) == NULL) {
-		Alert("out of memory in peer_session_create().\n");
-		goto out_free_sess;
-	}
-	t->nice = l->nice;
-
-	if ((s = stream_new(sess, t, &appctx->obj_type)) == NULL) {
+	if ((s = stream_new(sess, &appctx->obj_type)) == NULL) {
 		Alert("Failed to initialize stream in peer_session_create().\n");
-		goto out_free_task;
+		goto out_free_sess;
 	}
 
 	/* The tasks below are normally what is supposed to be done by
@@ -1851,7 +1844,7 @@ static struct appctx *peer_session_create(struct peers *peers, struct peer *peer
 	totalconn++;
 
 	peer->appctx = appctx;
-	task_wakeup(t, TASK_WOKEN_INIT);
+	task_wakeup(s->task, TASK_WOKEN_INIT);
 	return appctx;
 
 	/* Error unrolling */
@@ -1859,8 +1852,6 @@ static struct appctx *peer_session_create(struct peers *peers, struct peer *peer
 	LIST_DEL(&s->by_sess);
 	LIST_DEL(&s->list);
 	pool_free2(pool2_stream, s);
- out_free_task:
-	task_free(t);
  out_free_sess:
 	session_free(sess);
  out_free_appctx:
diff --git a/src/session.c b/src/session.c
index cc2a0b87a..ea4e020a6 100644
--- a/src/session.c
+++ b/src/session.c
@@ -109,7 +109,7 @@ int session_accept_fd(struct listener *l, int cfd, struct sockaddr_storage *addr
 	struct connection *cli_conn;
 	struct proxy *p = l->bind_conf->frontend;
 	struct session *sess;
-	struct task *t;
+	struct stream *strm;
 	int ret;
 
 
@@ -222,12 +222,6 @@ int session_accept_fd(struct listener *l, int cfd, struct sockaddr_storage *addr
 	if (global.tune.client_rcvbuf)
 		setsockopt(cfd, SOL_SOCKET, SO_RCVBUF, &global.tune.client_rcvbuf, sizeof(global.tune.client_rcvbuf));
 
-	if (unlikely((t = task_new()) == NULL))
-		goto out_free_sess;
-
-	t->context = sess;
-	t->nice = l->nice;
-
 	/* OK, now either we have a pending handshake to execute with and
 	 * then we must return to the I/O layer, or we can proceed with the
 	 * end of the stream initialization. In case of handshake, we also
@@ -241,10 +235,18 @@ int session_accept_fd(struct listener *l, int cfd, struct sockaddr_storage *addr
 	 *          conn -- owner ---> task
 	 */
 	if (cli_conn->flags & CO_FL_HANDSHAKE) {
+		struct task *t;
+
+		if (unlikely((t = task_new()) == NULL))
+			goto out_free_sess;
+
 		conn_set_owner(cli_conn, t);
 		conn_set_xprt_done_cb(cli_conn, conn_complete_session);
+
+		t->context = sess;
+		t->nice    = l->nice;
 		t->process = session_expire_embryonic;
-		t->expire = tick_add_ifset(now_ms, p->timeout.client);
+		t->expire  = tick_add_ifset(now_ms, p->timeout.client);
 		task_queue(t);
 		return 1;
 	}
@@ -261,14 +263,12 @@ int session_accept_fd(struct listener *l, int cfd, struct sockaddr_storage *addr
 		goto out_free_sess;
 
 	session_count_new(sess);
-	if (!stream_new(sess, t, &cli_conn->obj_type))
-		goto out_free_task;
+	if ((strm = stream_new(sess, &cli_conn->obj_type)) == NULL)
+		goto out_free_sess;
 
-	task_wakeup(t, TASK_WOKEN_INIT);
+	task_wakeup(strm->task, TASK_WOKEN_INIT);
 	return 1;
 
- out_free_task:
-	task_free(t);
  out_free_sess:
 	p->feconn--;
 	session_free(sess);
@@ -412,6 +412,7 @@ static int conn_complete_session(struct connection *conn)
 {
 	struct task *task = conn->owner;
 	struct session *sess = task->context;
+	struct stream *strm;
 
 	conn_clear_xprt_done_cb(conn);
 
@@ -430,11 +431,14 @@ static int conn_complete_session(struct connection *conn)
 		goto fail;
 
 	session_count_new(sess);
-	task->process = sess->listener->handler;
-	if (!stream_new(sess, task, &conn->obj_type))
+	if ((strm = stream_new(sess, &conn->obj_type)) == NULL)
 		goto fail;
 
-	task_wakeup(task, TASK_WOKEN_INIT);
+	task_wakeup(strm->task, TASK_WOKEN_INIT);
+
+	/* the embryonic session's task is not needed anymore */
+	task_delete(task);
+	task_free(task);
 	return 0;
 
  fail:
diff --git a/src/stream.c b/src/stream.c
index 6f7a1be64..8527c297f 100644
--- a/src/stream.c
+++ b/src/stream.c
@@ -67,20 +67,22 @@ static struct list service_keywords = LIST_HEAD_INIT(service_keywords);
 
 /* This function is called from the session handler which detects the end of
  * handshake, in order to complete initialization of a valid stream. It must be
- * called with a session (which may be embryonic). It returns the pointer to
+ * called with a completley initialized session. It returns the pointer to
  * the newly created stream, or NULL in case of fatal error. The client-facing
- * end point is assigned to <origin>, which must be valid. The task's context
- * is set to the new stream, and its function is set to process_stream().
- * Target and analysers are null.
+ * end point is assigned to <origin>, which must be valid. The stream's task
+ * is configured with a nice value inherited from the listener's nice if any.
+ * The task's context is set to the new stream, and its function is set to
+ * process_stream(). Target and analysers are null.
  */
-struct stream *stream_new(struct session *sess, struct task *t, enum obj_type *origin)
+struct stream *stream_new(struct session *sess, enum obj_type *origin)
 {
 	struct stream *s;
+	struct task *t;
 	struct connection *conn = objt_conn(origin);
 	struct appctx *appctx   = objt_appctx(origin);
 
 	if (unlikely((s = pool_alloc2(pool2_stream)) == NULL))
-		return s;
+		goto out_fail_alloc;
 
 	/* minimum stream initialization required for an embryonic stream is
 	 * fairly low. We need very little to execute L4 ACLs, then we need a
@@ -145,11 +147,16 @@ struct stream *stream_new(struct session *sess, struct task *t, enum obj_type *o
 	s->flags |= SF_INITIALIZED;
 	s->unique_id = NULL;
 
+	if ((t = task_new()) == NULL)
+		goto out_fail_alloc;
+
 	s->task = t;
 	s->pending_events = 0;
 	t->process = process_stream;
 	t->context = s;
 	t->expire = TICK_ETERNITY;
+	if (sess->listener)
+		t->nice = sess->listener->nice;
 
 	/* Note: initially, the stream's backend points to the frontend.
 	 * This changes later when switching rules are executed or
@@ -250,6 +257,8 @@ struct stream *stream_new(struct session *sess, struct task *t, enum obj_type *o
 	/* Error unrolling */
  out_fail_accept:
 	flt_stream_release(s, 0);
+	task_free(t);
+ out_fail_alloc:
 	LIST_DEL(&s->by_sess);
 	LIST_DEL(&s->list);
 	pool_free2(pool2_stream, s);