diff --git a/src/peers.c b/src/peers.c
index 4899ee7a0..d1a06d801 100644
--- a/src/peers.c
+++ b/src/peers.c
@@ -1166,17 +1166,8 @@ static struct stream *peer_session_create(struct peer *peer, struct peer_session
 	conn->target = s->target = &s->be->obj_type;
 	memcpy(&conn->addr.to, &peer->addr, sizeof(conn->addr.to));
 	s->do_log = NULL;
-
-	/* default error reporting function, may be changed by analysers */
-	s->srv_error = default_srv_error;
 	s->uniq_id = 0;
 
-	/* note: this should not happen anymore since there's always at least the switching rules */
-	if (!s->req.analysers) {
-		channel_auto_connect(&s->req);/* don't wait to establish connection */
-		channel_auto_close(&s->req);  /* let the producer forward close requests */
-	}
-
 	s->req.rto = s->sess->fe->timeout.client;
 	s->req.wto = s->be->timeout.server;
 	s->res.rto = s->be->timeout.server;
diff --git a/src/session.c b/src/session.c
index 247e4927d..6ae2592fe 100644
--- a/src/session.c
+++ b/src/session.c
@@ -88,6 +88,7 @@ int session_accept_fd(struct listener *l, int cfd, struct sockaddr_storage *addr
 	struct connection *cli_conn;
 	struct proxy *p = l->frontend;
 	struct session *sess;
+	struct stream *strm;
 	struct task *t;
 	int ret;
 
@@ -224,9 +225,15 @@ int session_accept_fd(struct listener *l, int cfd, struct sockaddr_storage *addr
 
 	/* OK let's complete stream initialization since there is no handshake */
 	cli_conn->flags |= CO_FL_CONNECTED;
-	if (stream_new(sess, t))
-		return 1;
+	strm = stream_new(sess, t);
+	if (!strm)
+		goto out_free_task;
 
+	strm->target        = sess->listener->default_target;
+	strm->req.analysers = sess->listener->analysers;
+	return 1;
+
+ out_free_task:
 	task_free(t);
  out_free_sess:
 	p->feconn--;
@@ -369,12 +376,22 @@ static int conn_complete_session(struct connection *conn)
 {
 	struct task *task = conn->owner;
 	struct session *sess = task->context;
+	struct stream *strm;
 
-	if (!(conn->flags & CO_FL_ERROR) && (stream_new(sess, task) != NULL)) {
-		conn->flags &= ~CO_FL_INIT_DATA;
-		return 0;
-	}
+	if (conn->flags & CO_FL_ERROR)
+		goto fail;
 
+	task->process = sess->listener->handler;
+	strm = stream_new(sess, task);
+	if (!strm)
+		goto fail;
+
+	strm->target        = sess->listener->default_target;
+	strm->req.analysers = sess->listener->analysers;
+	conn->flags &= ~CO_FL_INIT_DATA;
+	return 0;
+
+ fail:
 	session_kill_embryonic(sess);
 	return -1;
 }
diff --git a/src/stream.c b/src/stream.c
index dca1c8884..863075b0b 100644
--- a/src/stream.c
+++ b/src/stream.c
@@ -61,11 +61,12 @@ struct list buffer_wq = LIST_HEAD_INIT(buffer_wq);
  * be called with an embryonic session. It returns the pointer to the newly
  * created stream, or NULL in case of fatal error. For now the client-side
  * end point is taken from the session's 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.
  */
 struct stream *stream_new(struct session *sess, struct task *t)
 {
 	struct stream *s;
-	struct listener *l = sess->listener;
 	struct connection *conn = objt_conn(sess->origin);
 	struct appctx *appctx   = objt_appctx(sess->origin);
 	int i;
@@ -121,7 +122,7 @@ struct stream *stream_new(struct session *sess, struct task *t)
 	s->unique_id = NULL;
 
 	s->task = t;
-	t->process = l->handler;
+	t->process = process_stream;
 	t->context = s;
 	t->expire = TICK_ETERNITY;
 
@@ -136,7 +137,8 @@ struct stream *stream_new(struct session *sess, struct task *t)
 	s->res_cap = NULL;
 
 	/* Let's count a stream now */
-	proxy_inc_fe_sess_ctr(l, sess->fe);
+	if (conn)
+		proxy_inc_fe_sess_ctr(sess->listener, sess->fe);
 
 	for (i = 0; i < MAX_SESS_STKCTR; i++) {
 		void *ptr;
@@ -178,7 +180,7 @@ struct stream *stream_new(struct session *sess, struct task *t)
 		s->si[1].flags |= SI_FL_INDEP_STR;
 
 	stream_init_srv_conn(s);
-	s->target = l->default_target; /* used by peers and CLI */
+	s->target = NULL;
 	s->pend_pos = NULL;
 
 	/* init store persistence */
@@ -186,14 +188,9 @@ struct stream *stream_new(struct session *sess, struct task *t)
 
 	channel_init(&s->req);
 	s->req.flags |= CF_READ_ATTACHED; /* the producer is already connected */
-
-	/* activate default analysers enabled for this listener */
-	s->req.analysers = l->analysers;
-
-	if (!s->req.analysers) {
-		channel_auto_connect(&s->req);  /* don't wait to establish connection */
-		channel_auto_close(&s->req);    /* let the producer forward close requests */
-	}
+	s->req.analysers = 0;
+	channel_auto_connect(&s->req);  /* don't wait to establish connection */
+	channel_auto_close(&s->req);    /* let the producer forward close requests */
 
 	s->req.rto = sess->fe->timeout.client;
 	s->req.wto = TICK_ETERNITY;