diff --git a/src/frontend.c b/src/frontend.c
index f51a3d9ed..cbf617448 100644
--- a/src/frontend.c
+++ b/src/frontend.c
@@ -87,10 +87,9 @@ int frontend_accept(struct session *s)
 	s->srv_error = default_srv_error;
 
 	/* Adjust some socket options */
-	if ((s->listener->addr.ss_family != AF_UNIX) && unlikely(setsockopt(cfd, IPPROTO_TCP, TCP_NODELAY, (char *) &one, sizeof(one)) == -1)) {
-		Alert("accept(): cannot set the socket in non blocking mode. Giving up\n");
+	if ((s->listener->addr.ss_family != AF_UNIX) &&
+	    setsockopt(cfd, IPPROTO_TCP, TCP_NODELAY, (char *) &one, sizeof(one)) == -1)
 		goto out_delete_cfd;
-	}
 
 	if (s->fe->options & PR_O_TCP_CLI_KA)
 		setsockopt(cfd, SOL_SOCKET, SO_KEEPALIVE, (char *) &one, sizeof(one));
diff --git a/src/session.c b/src/session.c
index 5432266cd..d718695d4 100644
--- a/src/session.c
+++ b/src/session.c
@@ -57,10 +57,8 @@ int session_accept(struct listener *l, int cfd, struct sockaddr_storage *addr)
 	struct http_txn *txn;
 	struct task *t;
 
-	if (unlikely((s = pool_alloc2(pool2_session)) == NULL)) {
-		Alert("out of memory in event_accept().\n");
+	if (unlikely((s = pool_alloc2(pool2_session)) == NULL))
 		goto out_close;
-	}
 
 	/* minimum session initialization required for monitor mode below */
 	s->flags = 0;
@@ -89,10 +87,8 @@ int session_accept(struct listener *l, int cfd, struct sockaddr_storage *addr)
 	LIST_ADDQ(&sessions, &s->list);
 	LIST_INIT(&s->back_refs);
 
-	if (unlikely((t = task_new()) == NULL)) { /* disable this proxy for a while */
-		Alert("out of memory in event_accept().\n");
+	if (unlikely((t = task_new()) == NULL))
 		goto out_free_session;
-	}
 
 	s->term_trace = 0;
 	s->cli_addr = *addr;
@@ -211,10 +207,8 @@ int session_accept(struct listener *l, int cfd, struct sockaddr_storage *addr)
 	s->store_count = 0;
 
 	/* Adjust some socket options */
-	if (unlikely(fcntl(cfd, F_SETFL, O_NONBLOCK) == -1)) {
-		Alert("accept(): cannot set the socket in non blocking mode. Giving up\n");
+	if (unlikely(fcntl(cfd, F_SETFL, O_NONBLOCK) == -1))
 		goto out_free_task;
-	}
 
 	txn = &s->txn;
 	/* Those variables will be checked and freed if non-NULL in
diff --git a/src/stream_sock.c b/src/stream_sock.c
index 362470216..46dfeba9b 100644
--- a/src/stream_sock.c
+++ b/src/stream_sock.c
@@ -1188,7 +1188,9 @@ int stream_sock_accept(int fd)
 		}
 
 		if (unlikely(cfd >= global.maxsock)) {
-			Alert("accept(): not enough free sockets. Raise -n argument. Giving up.\n");
+			send_log(p, LOG_EMERG,
+				 "Proxy %s reached the configured maximum connection limit. Please check the global 'maxconn' value.\n",
+				 p->id);
 			goto out_close;
 		}