diff --git a/include/proto/queue.h b/include/proto/queue.h
index be78b53..77964fe 100644
--- a/include/proto/queue.h
+++ b/include/proto/queue.h
@@ -64,11 +64,11 @@
 }
 
 /* returns 0 if nothing has to be done for server <s> regarding queued connections,
- * and non-zero otherwise. If the server is down, we always return zero. Suited for
- * and if/else usage.
+ * and non-zero otherwise. If the server is down, we only check its own queue. Suited
+ * for and if/else usage.
  */
 static inline int may_dequeue_tasks(const struct server *s, const struct proxy *p) {
-	return (s && (s->state & SRV_RUNNING) && (s->nbpend || p->nbpend) &&
+	return (s && (s->nbpend || (p->nbpend && (s->state & SRV_RUNNING))) &&
 		(!s->maxconn || s->cur_sess < srv_dynamic_maxconn(s)));
 }
 
diff --git a/src/queue.c b/src/queue.c
index 172e056..fe94043 100644
--- a/src/queue.c
+++ b/src/queue.c
@@ -86,6 +86,10 @@
  * returned. Note that neither <srv> nor <px> may be NULL.
  * Priority is given to the oldest request in the queue if both <srv> and <px>
  * have pending requests. This ensures that no request will be left unserved.
+ * The <px> queue is not considered if the server is not RUNNING. The <srv>
+ * queue is still considered in this case, because if some connections remain
+ * there, it means that some requests have been forced there after it was seen
+ * down (eg: due to option persist).
  * The session is immediately marked as "assigned", and both its <srv> and
  * <srv_conn> are set to <srv>,
  */
@@ -97,7 +101,7 @@
 	ps = pendconn_from_srv(srv);
 	pp = pendconn_from_px(px);
 	/* we want to get the definitive pendconn in <ps> */
-	if (!pp) {
+	if (!pp || !(srv->state & SRV_RUNNING)) {
 		if (!ps)
 			return NULL;
 	} else {
diff --git a/src/session.c b/src/session.c
index c0df6c6..5046e04 100644
--- a/src/session.c
+++ b/src/session.c
@@ -46,13 +46,16 @@
 
 	if (s->pend_pos)
 		pendconn_free(s->pend_pos);
+
 	if (s->srv) { /* there may be requests left pending in queue */
 		if (s->flags & SN_CURR_SESS) {
 			s->flags &= ~SN_CURR_SESS;
 			s->srv->cur_sess--;
 		}
-		process_srv_queue(s->srv);
+		if (may_dequeue_tasks(s->srv, s->be))
+			process_srv_queue(s->srv);
 	}
+
 	if (unlikely(s->srv_conn)) {
 		/* the session still has a reserved slot on a server, but
 		 * it should normally be only the same as the one above,