diff --git a/include/proto/stream.h b/include/proto/stream.h
index 02992fd51..820cf4747 100644
--- a/include/proto/stream.h
+++ b/include/proto/stream.h
@@ -36,7 +36,7 @@ extern struct list buffer_wq;
 
 extern struct data_cb sess_conn_cb;
 
-int stream_accept_session(struct session *sess, struct task *t);
+struct stream *stream_new(struct session *sess, struct task *t);
 
 /* perform minimal intializations, report 0 in case of error, 1 if OK. */
 int init_stream();
diff --git a/src/peers.c b/src/peers.c
index 1b0fa1047..4899ee7a0 100644
--- a/src/peers.c
+++ b/src/peers.c
@@ -1140,7 +1140,7 @@ static struct stream *peer_session_create(struct peer *peer, struct peer_session
 	}
 	t->nice = l->nice;
 
-	if (stream_accept_session(sess, t) <= 0) {
+	if ((s = stream_new(sess, t)) == NULL) {
 		Alert("Failed to initialize stream in peer_session_create().\n");
 		goto out_free_task;
 	}
@@ -1148,7 +1148,6 @@ static struct stream *peer_session_create(struct peer *peer, struct peer_session
 	/* The tasks below are normally what is supposed to be done by
 	 * fe->accept().
 	 */
-	s = t->context;   // For now the session is not stored anywhere else :-/
 	s->flags = SF_ASSIGNED|SF_ADDR_SET;
 
 	/* initiate an outgoing connection */
diff --git a/src/session.c b/src/session.c
index 790f89aed..6dcbadb4c 100644
--- a/src/session.c
+++ b/src/session.c
@@ -195,9 +195,8 @@ 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;
-	ret = stream_accept_session(sess, t);
-	if (ret > 0)
-		return ret;
+	if (stream_new(sess, t))
+		return 1;
 
 	task_free(t);
  out_free_sess:
@@ -342,7 +341,7 @@ static int conn_complete_session(struct connection *conn)
 	struct task *task = conn->owner;
 	struct session *sess = task->context;
 
-	if (!(conn->flags & CO_FL_ERROR) && (stream_accept_session(sess, task) > 0)) {
+	if (!(conn->flags & CO_FL_ERROR) && (stream_new(sess, task) != NULL)) {
 		conn->flags &= ~CO_FL_INIT_DATA;
 		return 0;
 	}
diff --git a/src/stream.c b/src/stream.c
index 1bcd2eb90..3e2b5b663 100644
--- a/src/stream.c
+++ b/src/stream.c
@@ -58,26 +58,21 @@ struct list buffer_wq = LIST_HEAD_INIT(buffer_wq);
 
 /* 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 an embryonic session. It returns a positive value upon
- * success, 0 if the connection can be ignored, or a negative value upon
- * critical failure. The accepted file descriptor is closed if we return <= 0.
- * The client-side end point is assumed to be a connection, whose pointer is
- * taken from sess->origin which is assumed to be valid.
+ * 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.
  */
-int stream_accept_session(struct session *sess, struct task *t)
+struct stream *stream_new(struct session *sess, struct task *t)
 {
 	struct stream *s;
 	struct listener *l = sess->listener;
 	struct proxy *p = sess->fe;
 	struct connection *conn = objt_conn(sess->origin);
 	struct appctx *appctx   = objt_appctx(sess->origin);
-	int ret;
 	int i;
 
-	ret = -1; /* assume unrecoverable error by default */
-
 	if (unlikely((s = pool_alloc2(pool2_stream)) == NULL))
-		goto out_return;
+		return s;
 
 	/* minimum stream initialization required for an embryonic stream is
 	 * fairly low. We need very little to execute L4 ACLs, then we need a
@@ -230,14 +225,13 @@ int stream_accept_session(struct session *sess, struct task *t)
 	 * priorities to tasks.
 	 */
 	task_wakeup(t, TASK_WOKEN_INIT);
-	return 1;
+	return s;
 
 	/* Error unrolling */
  out_fail_accept:
 	LIST_DEL(&s->list);
 	pool_free2(pool2_stream, s);
- out_return:
-	return ret;
+	return NULL;
 }
 
 /*