diff --git a/include/haproxy/connection-t.h b/include/haproxy/connection-t.h
index 6cc62ee78..3c65013bf 100644
--- a/include/haproxy/connection-t.h
+++ b/include/haproxy/connection-t.h
@@ -547,7 +547,7 @@ struct connection {
 		struct mt_list toremove_list; /* list element when idle connection is ready to be purged */
 	};
 	union {
-		struct list session_list;  /* used by backend conns, list of attached connections to a session */
+		struct list sess_el;       /* used by private backend conns, list elem into session */
 		struct list stopping_list; /* used by frontend conns, attach point in mux stopping list */
 	};
 	union conn_handle handle;     /* connection handle at the socket layer */
diff --git a/include/haproxy/session-t.h b/include/haproxy/session-t.h
index dff167ecb..bf0079129 100644
--- a/include/haproxy/session-t.h
+++ b/include/haproxy/session-t.h
@@ -57,15 +57,16 @@ struct session {
 	long t_idle;                    /* idle duration, -1 if never occurs */
 	int idle_conns;                 /* Number of connections we're currently responsible for that we are not using */
 	unsigned int flags;             /* session flags, SESS_FL_* */
-	struct list srv_list;           /* List of servers and the connections the session is currently responsible for */
+	struct list priv_conns;         /* list of private conns */
 	struct sockaddr_storage *src; /* source address (pool), when known, otherwise NULL */
 	struct sockaddr_storage *dst; /* destination address (pool), when known, otherwise NULL */
 };
 
-struct sess_srv_list {
-	void *target;
+/* List of private conns managed by a session, indexed by server */
+struct sess_priv_conns {
+	void *target;                   /* Server or dispatch used for indexing */
 	struct list conn_list;          /* Head of the connections list */
-	struct list srv_list;           /* Next element of the server list */
+	struct list sess_el;            /* Element of session.priv_conns */
 };
 
 #endif /* _HAPROXY_SESSION_T_H */
diff --git a/include/haproxy/session.h b/include/haproxy/session.h
index 5b080893e..90970e8e2 100644
--- a/include/haproxy/session.h
+++ b/include/haproxy/session.h
@@ -32,7 +32,7 @@
 #include <haproxy/stick_table.h>
 
 extern struct pool_head *pool_head_session;
-extern struct pool_head *pool_head_sess_srv_list;
+extern struct pool_head *pool_head_sess_priv_conns;
 
 struct session *session_new(struct proxy *fe, struct listener *li, enum obj_type *origin);
 void session_free(struct session *sess);
@@ -134,10 +134,12 @@ static inline void session_add_glitch_ctr(struct session *sess, uint inc)
 		__session_add_glitch_ctr(sess, inc);
 }
 
-/* Remove the connection from the session list, and destroy the srv_list if it's now empty */
+/* Remove the connection from the session list, and destroy sess_priv_conns
+ * element if it's now empty.
+ */
 static inline void session_unown_conn(struct session *sess, struct connection *conn)
 {
-	struct sess_srv_list *srv_list = NULL;
+	struct sess_priv_conns *pconns = NULL;
 
 	BUG_ON(objt_listener(conn->target));
 
@@ -148,56 +150,56 @@ static inline void session_unown_conn(struct session *sess, struct connection *c
 	 * conn->owner that points to a dead session, but in this case the
 	 * element is not linked.
 	 */
-	if (!LIST_INLIST(&conn->session_list))
+	if (!LIST_INLIST(&conn->sess_el))
 		return;
 
 	if (conn->flags & CO_FL_SESS_IDLE)
 		sess->idle_conns--;
-	LIST_DEL_INIT(&conn->session_list);
+	LIST_DEL_INIT(&conn->sess_el);
 	conn->owner = NULL;
-	list_for_each_entry(srv_list, &sess->srv_list, srv_list) {
-		if (srv_list->target == conn->target) {
-			if (LIST_ISEMPTY(&srv_list->conn_list)) {
-				LIST_DELETE(&srv_list->srv_list);
-				pool_free(pool_head_sess_srv_list, srv_list);
+	list_for_each_entry(pconns, &sess->priv_conns, sess_el) {
+		if (pconns->target == conn->target) {
+			if (LIST_ISEMPTY(&pconns->conn_list)) {
+				LIST_DELETE(&pconns->sess_el);
+				pool_free(pool_head_sess_priv_conns, pconns);
 			}
 			break;
 		}
 	}
 }
 
-/* Add the connection <conn> to the server list of the session <sess>. This
- * function is called only if the connection is private. Nothing is performed if
- * the connection is already in the session sever list or if the session does
- * not own the connection.
+/* Add the connection <conn> to the private conns list of session <sess>. This
+ * function is called only if the connection is private. Nothing is performed
+ * if the connection is already in the session list or if the session does not
+ * owned the connection.
  */
 static inline int session_add_conn(struct session *sess, struct connection *conn, void *target)
 {
-	struct sess_srv_list *srv_list = NULL;
+	struct sess_priv_conns *pconns = NULL;
 	int found = 0;
 
 	BUG_ON(objt_listener(conn->target));
 
 	/* Already attach to the session or not the connection owner */
-	if (!LIST_ISEMPTY(&conn->session_list) || (conn->owner && conn->owner != sess))
+	if (!LIST_ISEMPTY(&conn->sess_el) || (conn->owner && conn->owner != sess))
 		return 1;
 
-	list_for_each_entry(srv_list, &sess->srv_list, srv_list) {
-		if (srv_list->target == target) {
+	list_for_each_entry(pconns, &sess->priv_conns, sess_el) {
+		if (pconns->target == target) {
 			found = 1;
 			break;
 		}
 	}
 	if (!found) {
 		/* The session has no connection for the server, create a new entry */
-		srv_list = pool_alloc(pool_head_sess_srv_list);
-		if (!srv_list)
+		pconns = pool_alloc(pool_head_sess_priv_conns);
+		if (!pconns)
 			return 0;
-		srv_list->target = target;
-		LIST_INIT(&srv_list->conn_list);
-		LIST_APPEND(&sess->srv_list, &srv_list->srv_list);
+		pconns->target = target;
+		LIST_INIT(&pconns->conn_list);
+		LIST_APPEND(&sess->priv_conns, &pconns->sess_el);
 	}
-	LIST_APPEND(&srv_list->conn_list, &conn->session_list);
+	LIST_APPEND(&pconns->conn_list, &conn->sess_el);
 	return 1;
 }
 
@@ -230,11 +232,11 @@ static inline int session_check_idle_conn(struct session *sess, struct connectio
 static inline struct connection *session_get_conn(struct session *sess, void *target, int64_t hash)
 {
 	struct connection *srv_conn = NULL;
-	struct sess_srv_list *srv_list;
+	struct sess_priv_conns *pconns;
 
-	list_for_each_entry(srv_list, &sess->srv_list, srv_list) {
-		if (srv_list->target == target) {
-			list_for_each_entry(srv_conn, &srv_list->conn_list, session_list) {
+	list_for_each_entry(pconns, &sess->priv_conns, sess_el) {
+		if (pconns->target == target) {
+			list_for_each_entry(srv_conn, &pconns->conn_list, sess_el) {
 				if ((srv_conn->hash_node && srv_conn->hash_node->node.key == hash) &&
 				    srv_conn->mux &&
 				    (srv_conn->mux->avail_streams(srv_conn) > 0) &&
diff --git a/src/backend.c b/src/backend.c
index 4ef0087c3..7dd8ceb76 100644
--- a/src/backend.c
+++ b/src/backend.c
@@ -653,9 +653,9 @@ int assign_server(struct stream *s)
 	if ((s->be->lbprm.algo & BE_LB_KIND) != BE_LB_KIND_HI &&
 	    ((s->sess->flags & SESS_FL_PREFER_LAST) ||
 	     (s->be->options & PR_O_PREF_LAST))) {
-		struct sess_srv_list *srv_list;
-		list_for_each_entry(srv_list, &s->sess->srv_list, srv_list) {
-			struct server *tmpsrv = objt_server(srv_list->target);
+		struct sess_priv_conns *pconns;
+		list_for_each_entry(pconns, &s->sess->priv_conns, sess_el) {
+			struct server *tmpsrv = objt_server(pconns->target);
 
 			if (tmpsrv && tmpsrv->proxy == s->be &&
 			    ((s->sess->flags & SESS_FL_PREFER_LAST) ||
@@ -663,7 +663,7 @@ int assign_server(struct stream *s)
 			      server_has_room(tmpsrv) || (
 			      tmpsrv->queue.length + 1 < s->be->max_ka_queue))) &&
 			    srv_currently_usable(tmpsrv)) {
-				list_for_each_entry(conn, &srv_list->conn_list, session_list) {
+				list_for_each_entry(conn, &pconns->conn_list, sess_el) {
 					if (!(conn->flags & CO_FL_WAIT_XPRT)) {
 						srv = tmpsrv;
 						s->target = &srv->obj_type;
diff --git a/src/connection.c b/src/connection.c
index 2f2726b32..bbeea5e35 100644
--- a/src/connection.c
+++ b/src/connection.c
@@ -474,7 +474,7 @@ void conn_init(struct connection *conn, void *target)
 	conn->proxy_netns = NULL;
 	MT_LIST_INIT(&conn->toremove_list);
 	if (conn_is_back(conn))
-		LIST_INIT(&conn->session_list);
+		LIST_INIT(&conn->sess_el);
 	else
 		LIST_INIT(&conn->stopping_list);
 	LIST_INIT(&conn->tlv_list);
@@ -513,7 +513,7 @@ static void conn_backend_deinit(struct connection *conn)
 {
 	/* If the connection is owned by the session, remove it from its list
 	 */
-	if (conn_is_back(conn) && LIST_INLIST(&conn->session_list)) {
+	if (conn_is_back(conn) && LIST_INLIST(&conn->sess_el)) {
 		session_unown_conn(conn->owner, conn);
 	}
 	else if (!(conn->flags & CO_FL_PRIVATE)) {
diff --git a/src/mux_fcgi.c b/src/mux_fcgi.c
index 0230e6b79..d192cf9d1 100644
--- a/src/mux_fcgi.c
+++ b/src/mux_fcgi.c
@@ -3619,7 +3619,7 @@ static void fcgi_detach(struct sedesc *sd)
 			}
 			else if (!fconn->conn->hash_node->node.node.leaf_p &&
 				 fcgi_avail_streams(fconn->conn) > 0 && objt_server(fconn->conn->target) &&
-				 !LIST_INLIST(&fconn->conn->session_list)) {
+				 !LIST_INLIST(&fconn->conn->sess_el)) {
 				srv_add_to_avail_list(__objt_server(fconn->conn->target), fconn->conn);
 			}
 		}
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 2a2a15d4f..d72fe6344 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -4858,7 +4858,7 @@ static void h2_detach(struct sedesc *sd)
 				}
 				else if (!h2c->conn->hash_node->node.node.leaf_p &&
 					 h2_avail_streams(h2c->conn) > 0 && objt_server(h2c->conn->target) &&
-					 !LIST_INLIST(&h2c->conn->session_list)) {
+					 !LIST_INLIST(&h2c->conn->sess_el)) {
 					srv_add_to_avail_list(__objt_server(h2c->conn->target), h2c->conn);
 				}
 			}
diff --git a/src/session.c b/src/session.c
index b85797a11..f54490e79 100644
--- a/src/session.c
+++ b/src/session.c
@@ -27,8 +27,8 @@
 
 
 DECLARE_POOL(pool_head_session, "session", sizeof(struct session));
-DECLARE_POOL(pool_head_sess_srv_list, "session server list",
-		sizeof(struct sess_srv_list));
+DECLARE_POOL(pool_head_sess_priv_conns, "session priv conns list",
+             sizeof(struct sess_priv_conns));
 
 int conn_complete_session(struct connection *conn);
 
@@ -61,7 +61,7 @@ struct session *session_new(struct proxy *fe, struct listener *li, enum obj_type
 		sess->t_idle = -1;
 		_HA_ATOMIC_INC(&totalconn);
 		_HA_ATOMIC_INC(&jobs);
-		LIST_INIT(&sess->srv_list);
+		LIST_INIT(&sess->priv_conns);
 		sess->idle_conns = 0;
 		sess->flags = SESS_FL_NONE;
 		sess->src = NULL;
@@ -76,7 +76,7 @@ struct session *session_new(struct proxy *fe, struct listener *li, enum obj_type
 void session_free(struct session *sess)
 {
 	struct connection *conn, *conn_back;
-	struct sess_srv_list *srv_list, *srv_list_back;
+	struct sess_priv_conns *pconns, *pconns_back;
 
 	if (sess->listener)
 		listener_release(sess->listener);
@@ -86,9 +86,9 @@ void session_free(struct session *sess)
 	conn = objt_conn(sess->origin);
 	if (conn != NULL && conn->mux)
 		conn->mux->destroy(conn->ctx);
-	list_for_each_entry_safe(srv_list, srv_list_back, &sess->srv_list, srv_list) {
-		list_for_each_entry_safe(conn, conn_back, &srv_list->conn_list, session_list) {
-			LIST_DEL_INIT(&conn->session_list);
+	list_for_each_entry_safe(pconns, pconns_back, &sess->priv_conns, sess_el) {
+		list_for_each_entry_safe(conn, conn_back, &pconns->conn_list, sess_el) {
+			LIST_DEL_INIT(&conn->sess_el);
 			if (conn->mux) {
 				conn->owner = NULL;
 				conn->flags &= ~CO_FL_SESS_IDLE;
@@ -102,7 +102,7 @@ void session_free(struct session *sess)
 				conn_free(conn);
 			}
 		}
-		pool_free(pool_head_sess_srv_list, srv_list);
+		pool_free(pool_head_sess_priv_conns, pconns);
 	}
 	sockaddr_free(&sess->src);
 	sockaddr_free(&sess->dst);
diff --git a/src/trace.c b/src/trace.c
index a233c0de1..d3a0b95ce 100644
--- a/src/trace.c
+++ b/src/trace.c
@@ -129,7 +129,7 @@ int __trace_enabled(enum trace_level level, uint64_t mask, struct trace_source *
 
 	if (!sess && strm)
 		sess = strm->sess;
-	else if (!sess && conn && LIST_INLIST(&conn->session_list))
+	else if (!sess && conn && LIST_INLIST(&conn->sess_el))
 		sess = conn->owner;
 	else if (!sess && check)
 		sess = check->sess;