diff --git a/src/mux_h2.c b/src/mux_h2.c
index 9bec15030..dba050552 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -1423,7 +1423,7 @@ static int h2_init(struct connection *conn, struct proxy *prx, struct session *s
 			goto fail_stream;
 	}
 
-	if (sess)
+	if (sess && !conn_is_back(conn))
 		proxy_inc_fe_cum_sess_ver_ctr(sess->listener, prx, 2);
 
 	/* Rhttp connections are only accounted after reverse completion. */
diff --git a/src/mux_quic.c b/src/mux_quic.c
index 0bc882e9c..68b913970 100644
--- a/src/mux_quic.c
+++ b/src/mux_quic.c
@@ -3515,7 +3515,7 @@ static int qmux_init(struct connection *conn, struct proxy *prx,
 		goto err;
 	}
 
-	if (qcc->app_ops == &h3_ops)
+	if (qcc->app_ops == &h3_ops && !conn_is_back(conn))
 		proxy_inc_fe_cum_sess_ver_ctr(sess->listener, prx, 3);
 
 	/* Register conn for idle front closing. This is done once everything is allocated. */