diff --git a/src/backend.c b/src/backend.c
index 97a62eb..2cf8c75 100644
--- a/src/backend.c
+++ b/src/backend.c
@@ -626,7 +626,7 @@
 			      tmpsrv->nbpend + 1 < s->be->max_ka_queue))) &&
 			    srv_currently_usable(tmpsrv)) {
 				list_for_each_entry(conn, &srv_list->conn_list, session_list) {
-					if (!(conn->flags & CO_FL_WAIT_L4L6)) {
+					if (!(conn->flags & CO_FL_WAIT_XPRT)) {
 						srv = tmpsrv;
 						s->target = &srv->obj_type;
 						goto out_ok;
@@ -1220,7 +1220,7 @@
 		}
 	}
 
-	if (((!reuse || (srv_conn && (srv_conn->flags & CO_FL_WAIT_L4L6)))
+	if (((!reuse || (srv_conn && (srv_conn->flags & CO_FL_WAIT_XPRT)))
 	    && ha_used_fds > global.tune.pool_high_count) && srv && srv->idle_orphan_conns) {
 		struct connection *tokill_conn;
 
@@ -1934,7 +1934,7 @@
 	}
 
 	/* first, let's see if we've made any progress on this connection */
-	if (!conn->mux && !(conn->flags & CO_FL_WAIT_L4L6)) {
+	if (!conn->mux && !(conn->flags & CO_FL_WAIT_XPRT)) {
 		/* connection finished to set up */
 		struct server *srv;
 
diff --git a/src/checks.c b/src/checks.c
index 2a495ef..233d754 100644
--- a/src/checks.c
+++ b/src/checks.c
@@ -886,7 +886,7 @@
 	}
 
 	/* the rest of the code below expects the connection to be ready! */
-	if (conn->flags & CO_FL_WAIT_L4L6 && !done)
+	if (conn->flags & CO_FL_WAIT_XPRT && !done)
 		goto wait_more_data;
 
 	/* Intermediate or complete response received.
@@ -1392,7 +1392,7 @@
 
 	default:
 		/* good connection is enough for pure TCP check */
-		if (!(conn->flags & CO_FL_WAIT_L4L6) && !check->type) {
+		if (!(conn->flags & CO_FL_WAIT_XPRT) && !check->type) {
 			if (check->use_ssl)
 				set_server_check_status(check, HCHK_STATUS_L6OK, NULL);
 			else
@@ -1477,7 +1477,7 @@
 		chk_report_conn_err(check, errno, 0);
 		task_wakeup(check->task, TASK_WOKEN_IO);
 	}
-	else if (!(conn->flags & CO_FL_HANDSHAKE) && !check->type) {
+	else if (!(conn->flags & CO_FL_WAIT_XPRT) && !check->type) {
 		/* we may get here if only a connection probe was required : we
 		 * don't have any data to send nor anything expected in response,
 		 * so the completion of the connection establishment is enough.
@@ -2285,7 +2285,7 @@
 				 * sending since otherwise we won't be woken up.
 				 */
 				__event_srv_chk_w(cs);
-				if (!(conn->flags & CO_FL_WAIT_L4_CONN) ||
+				if (!(conn->flags & CO_FL_WAIT_XPRT) ||
 				    !(check->wait_list.events & SUB_RETRY_SEND))
 					__event_srv_chk_r(cs);
 			}
@@ -2352,7 +2352,7 @@
 		 */
 		if (check->result == CHK_RES_UNKNOWN) {
 			/* good connection is enough for pure TCP check */
-			if (!(conn->flags & CO_FL_WAIT_L4L6) && !check->type) {
+			if (!(conn->flags & CO_FL_WAIT_XPRT) && !check->type) {
 				if (check->use_ssl)
 					set_server_check_status(check, HCHK_STATUS_L6OK, NULL);
 				else
@@ -2785,7 +2785,7 @@
 		next = LIST_NEXT(&next->list, struct tcpcheck_rule *, list);
 
 	if ((check->current_step || &next->list == head) &&
-	    (conn->flags & (CO_FL_WAIT_L4L6 | CO_FL_HANDSHAKE))) {
+	    (conn->flags & CO_FL_WAIT_XPRT)) {
 		/* we allow up to min(inter, timeout.connect) for a connection
 		 * to establish but only when timeout.check is set
 		 * as it may be to short for a full check otherwise
@@ -3034,7 +3034,7 @@
 				break;
 
 			/* don't do anything until the connection is established */
-			if (conn->flags & CO_FL_WAIT_L4L6)
+			if (conn->flags & CO_FL_WAIT_XPRT)
 				break;
 
 		} /* end 'connect' */
@@ -3233,7 +3233,7 @@
 	} /* end loop over double chained step list */
 
 	/* don't do anything until the connection is established */
-	if (conn->flags & CO_FL_WAIT_L4L6) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		/* update expire time, should be done by process_chk */
 		/* we allow up to min(inter, timeout.connect) for a connection
 		 * to establish but only when timeout.check is set
diff --git a/src/connection.c b/src/connection.c
index 319f85e..dcecf14 100644
--- a/src/connection.c
+++ b/src/connection.c
@@ -136,7 +136,7 @@
 	 * informations to create one, typically from the ALPN. If we're
 	 * done with the handshake, attempt to create one.
 	 */
-	if (unlikely(!conn->mux) && !(conn->flags & CO_FL_HANDSHAKE))
+	if (unlikely(!conn->mux) && !(conn->flags & CO_FL_WAIT_XPRT))
 		if (conn_create_mux(conn) < 0)
 			return;
 
@@ -155,9 +155,8 @@
 	 * Note that the wake callback is allowed to release the connection and
 	 * the fd (and return < 0 in this case).
 	 */
-	if ((io_available || (((conn->flags ^ flags) & CO_FL_NOTIFY_DONE) ||
-	     ((flags & (CO_FL_WAIT_L4L6|CO_FL_HANDSHAKE)) &&
-	      (conn->flags & (CO_FL_WAIT_L4L6|CO_FL_HANDSHAKE)) == 0))) &&
+	if ((io_available || ((conn->flags ^ flags) & CO_FL_NOTIFY_DONE) ||
+	     ((flags & CO_FL_WAIT_XPRT) && !(conn->flags & CO_FL_WAIT_XPRT))) &&
 	    conn->mux && conn->mux->wake && conn->mux->wake(conn) < 0)
 		return;
 
@@ -1530,7 +1529,7 @@
 	if (!conn)
 		return 0;
 
-	if (conn->flags & CO_FL_WAIT_L4L6) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -1551,7 +1550,7 @@
 	if (!conn)
 		return 0;
 
-	if (conn->flags & CO_FL_WAIT_L4L6) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
diff --git a/src/mux_fcgi.c b/src/mux_fcgi.c
index 85bc2cb..3fb85b5 100644
--- a/src/mux_fcgi.c
+++ b/src/mux_fcgi.c
@@ -2770,7 +2770,7 @@
 	}
 
 
-	if (conn->flags & (CO_FL_HANDSHAKE|CO_FL_WAIT_L4_CONN|CO_FL_WAIT_L6_CONN)) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		/* a handshake was requested */
 		goto schedule;
 	}
@@ -2954,7 +2954,7 @@
 	 * any stream that was waiting for it.
 	 */
 	if (!(fconn->flags & FCGI_CF_WAIT_FOR_HS) &&
-	    (conn->flags & (CO_FL_EARLY_SSL_HS | CO_FL_HANDSHAKE | CO_FL_EARLY_DATA)) == CO_FL_EARLY_DATA) {
+	    (conn->flags & (CO_FL_EARLY_SSL_HS | CO_FL_WAIT_XPRT | CO_FL_EARLY_DATA)) == CO_FL_EARLY_DATA) {
 		struct eb32_node *node;
 		struct fcgi_strm *fstrm;
 
@@ -3016,7 +3016,7 @@
 	int ret = 0;
 	switch (mux_ctl) {
 	case MUX_STATUS:
-		if (!(conn->flags & CO_FL_WAIT_L4L6))
+		if (!(conn->flags & CO_FL_WAIT_XPRT))
 			ret |= MUX_STATUS_READY;
 		return ret;
 	default:
diff --git a/src/mux_h1.c b/src/mux_h1.c
index eee595c..212a279 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -2667,7 +2667,7 @@
 	 * now, as we don't want to remove everything from the channel buffer
 	 * before we're sure we can send it.
 	 */
-	if (h1c->conn->flags & (CO_FL_WAIT_L4L6|CO_FL_HANDSHAKE)) {
+	if (h1c->conn->flags & CO_FL_WAIT_XPRT) {
 		TRACE_LEAVE(H1_EV_STRM_SEND, h1c->conn, h1s);
 		return 0;
 	}
@@ -2781,7 +2781,7 @@
 	int ret = 0;
 	switch (mux_ctl) {
 	case MUX_STATUS:
-		if (!(conn->flags & CO_FL_WAIT_L4L6))
+		if (!(conn->flags & CO_FL_WAIT_XPRT))
 			ret |= MUX_STATUS_READY;
 		return ret;
 	default:
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 9c1a77e..1a1d2ff 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -3425,7 +3425,7 @@
 		return 1;
 	}
 
-	if (conn->flags & (CO_FL_HANDSHAKE|CO_FL_WAIT_L4_CONN|CO_FL_WAIT_L6_CONN)) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		/* a handshake was requested */
 		goto schedule;
 	}
@@ -3578,7 +3578,7 @@
 	 * any stream that was waiting for it.
 	 */
 	if (!(h2c->flags & H2_CF_WAIT_FOR_HS) &&
-	    (conn->flags & (CO_FL_EARLY_SSL_HS | CO_FL_HANDSHAKE | CO_FL_EARLY_DATA)) == CO_FL_EARLY_DATA) {
+	    (conn->flags & (CO_FL_EARLY_SSL_HS | CO_FL_WAIT_XPRT | CO_FL_EARLY_DATA)) == CO_FL_EARLY_DATA) {
 		struct eb32_node *node;
 		struct h2s *h2s;
 
diff --git a/src/mux_pt.c b/src/mux_pt.c
index d9da001..4418a65 100644
--- a/src/mux_pt.c
+++ b/src/mux_pt.c
@@ -150,7 +150,7 @@
 	/* If we had early data, and we're done with the handshake
 	 * then whe know the data are safe, and we can remove the flag.
 	 */
-	if ((conn->flags & (CO_FL_EARLY_DATA | CO_FL_EARLY_SSL_HS | CO_FL_HANDSHAKE)) ==
+	if ((conn->flags & (CO_FL_EARLY_DATA | CO_FL_EARLY_SSL_HS | CO_FL_WAIT_XPRT)) ==
 	    CO_FL_EARLY_DATA)
 		conn->flags &= ~CO_FL_EARLY_DATA;
 	return ret;
@@ -348,7 +348,7 @@
 	int ret = 0;
 	switch (mux_ctl) {
 	case MUX_STATUS:
-		if (!(conn->flags & CO_FL_WAIT_L4L6))
+		if (!(conn->flags & CO_FL_WAIT_XPRT))
 			ret |= MUX_STATUS_READY;
 		return ret;
 	default:
diff --git a/src/session.c b/src/session.c
index d80392d..c62cc10 100644
--- a/src/session.c
+++ b/src/session.c
@@ -270,7 +270,7 @@
 	 *           v       |           |        |
 	 *          conn -- owner ---> task <-----+
 	 */
-	if (cli_conn->flags & (CO_FL_HANDSHAKE | CO_FL_EARLY_SSL_HS)) {
+	if (cli_conn->flags & (CO_FL_WAIT_XPRT | CO_FL_EARLY_SSL_HS)) {
 		if (unlikely((sess->task = task_new(tid_bit)) == NULL))
 			goto out_free_sess;
 
diff --git a/src/ssl_sock.c b/src/ssl_sock.c
index dafd258..cbf51b7 100644
--- a/src/ssl_sock.c
+++ b/src/ssl_sock.c
@@ -6517,7 +6517,7 @@
 	}
 #endif
 
-	if (conn->flags & (CO_FL_HANDSHAKE | CO_FL_SSL_WAIT_HS))
+	if (conn->flags & (CO_FL_WAIT_XPRT | CO_FL_SSL_WAIT_HS))
 		/* a handshake was requested */
 		return 0;
 
@@ -6628,7 +6628,7 @@
 	if (!ctx)
 		goto out_error;
 
-	if (conn->flags & (CO_FL_HANDSHAKE | CO_FL_SSL_WAIT_HS | CO_FL_EARLY_SSL_HS))
+	if (conn->flags & (CO_FL_WAIT_XPRT | CO_FL_SSL_WAIT_HS | CO_FL_EARLY_SSL_HS))
 		/* a handshake was requested */
 		return 0;
 
@@ -6830,7 +6830,7 @@
 {
 	struct ssl_sock_ctx *ctx = xprt_ctx;
 
-	if (conn->flags & (CO_FL_HANDSHAKE | CO_FL_SSL_WAIT_HS))
+	if (conn->flags & (CO_FL_WAIT_XPRT | CO_FL_SSL_WAIT_HS))
 		return;
 	if (!clean)
 		/* don't sent notify on SSL_shutdown */
@@ -7411,7 +7411,7 @@
 
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7442,7 +7442,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7489,7 +7489,7 @@
 
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7536,7 +7536,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7582,7 +7582,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7628,7 +7628,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7690,7 +7690,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7736,7 +7736,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7792,7 +7792,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7825,7 +7825,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7865,7 +7865,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -7917,7 +7917,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -8397,7 +8397,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags |= SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -8435,7 +8435,7 @@
 		return 0;
 	ctx = conn->xprt_ctx;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags = SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -8458,7 +8458,7 @@
 	if (!conn || conn->xprt != &ssl_sock)
 		return 0;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags = SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -8482,7 +8482,7 @@
 	if (!conn || conn->xprt != &ssl_sock)
 		return 0;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags = SMP_F_MAY_CHANGE;
 		return 0;
 	}
@@ -8507,7 +8507,7 @@
 	if (!conn || conn->xprt != &ssl_sock)
 		return 0;
 
-	if (conn->flags & CO_FL_WAIT_L6_CONN) {
+	if (conn->flags & CO_FL_WAIT_XPRT) {
 		smp->flags = SMP_F_MAY_CHANGE;
 		return 0;
 	}
diff --git a/src/stream_interface.c b/src/stream_interface.c
index 16bd3f8..0a2e7d1 100644
--- a/src/stream_interface.c
+++ b/src/stream_interface.c
@@ -451,7 +451,7 @@
 		struct connection *conn = objt_cs(si->end) ? objt_cs(si->end)->conn : NULL;
 
 		if (((oc->flags & (CF_SHUTW|CF_SHUTW_NOW)) == CF_SHUTW_NOW) &&
-		    (si->state == SI_ST_EST) && (!conn || !(conn->flags & (CO_FL_HANDSHAKE | CO_FL_EARLY_SSL_HS))))
+		    (si->state == SI_ST_EST) && (!conn || !(conn->flags & (CO_FL_WAIT_XPRT | CO_FL_EARLY_SSL_HS))))
 			si_shutw(si);
 		oc->wex = TICK_ETERNITY;
 	}
@@ -607,14 +607,14 @@
 	 * in the event there's an analyser waiting for the end of
 	 * the handshake.
 	 */
-	if (!(conn->flags & (CO_FL_HANDSHAKE | CO_FL_EARLY_SSL_HS)) &&
+	if (!(conn->flags & (CO_FL_WAIT_XPRT | CO_FL_EARLY_SSL_HS)) &&
 	    (cs->flags & CS_FL_WAIT_FOR_HS)) {
 		cs->flags &= ~CS_FL_WAIT_FOR_HS;
 		task_wakeup(si_task(si), TASK_WOKEN_MSG);
 	}
 
 	if (!si_state_in(si->state, SI_SB_EST|SI_SB_DIS|SI_SB_CLO) &&
-	    (conn->flags & (CO_FL_WAIT_L4L6 | CO_FL_HANDSHAKE)) == 0) {
+	    (conn->flags & CO_FL_WAIT_XPRT) == 0) {
 		si->exp = TICK_ETERNITY;
 		oc->flags |= CF_WRITE_NULL;
 		if (si->state == SI_ST_CON)