diff --git a/include/haproxy/quic_conn.h b/include/haproxy/quic_conn.h
index 640fe5bcc..6263231c5 100644
--- a/include/haproxy/quic_conn.h
+++ b/include/haproxy/quic_conn.h
@@ -606,20 +606,6 @@ int qc_parse_hd_form(struct quic_rx_packet *pkt,
 int quic_dgram_parse(struct quic_dgram *dgram, struct quic_conn *qc,
                      struct listener *li);
 
-/* Wake up every QUIC connections on closing/draining state if process stopping
- * is active. They will be immediately released so this ensures haproxy process
- * stopping is not delayed by them.
- */
-static inline void quic_handle_stopping(void)
-{
-	struct quic_conn *qc;
-
-	if (stopping) {
-		list_for_each_entry(qc, &th_ctx->quic_conns_clo, el_th_ctx)
-			task_wakeup(qc->idle_timer_task, TASK_WOKEN_OTHER);
-	}
-}
-
 int qc_set_tid_affinity(struct quic_conn *qc, uint new_tid, struct listener *new_li);
 void qc_finalize_affinity_rebind(struct quic_conn *qc);
 
diff --git a/src/haproxy.c b/src/haproxy.c
index 33e8ae867..935cb52e8 100644
--- a/src/haproxy.c
+++ b/src/haproxy.c
@@ -2995,9 +2995,6 @@ void run_poll_loop()
 				/* stop muxes/quic-conns before acknowledging stopping */
 				if (!(tg_ctx->stopping_threads & ti->ltid_bit)) {
 					task_wakeup(mux_stopping_data[tid].task, TASK_WOKEN_OTHER);
-#ifdef USE_QUIC
-					quic_handle_stopping();
-#endif
 					wake = 1;
 				}
 
diff --git a/src/quic_conn.c b/src/quic_conn.c
index 9bceea7e6..4994cb89a 100644
--- a/src/quic_conn.c
+++ b/src/quic_conn.c
@@ -2021,9 +2021,11 @@ void qc_finalize_affinity_rebind(struct quic_conn *qc)
 	BUG_ON(!(qc->flags & QUIC_FL_CONN_AFFINITY_CHANGED));
 	qc->flags &= ~QUIC_FL_CONN_AFFINITY_CHANGED;
 
-	/* A connection must not pass to closing state until affinity rebind
-	 * is completed. Else quic_handle_stopping() may miss it during process
-	 * stopping cleanup.
+	/* If quic_conn is closing it is unnecessary to migrate it as it will
+	 * be soon released. Besides, special care must be taken for CLOSING
+	 * connections (using quic_cc_conn and th_ctx.quic_conns_clo list for
+	 * instance). This should never occur as CLOSING connections are
+	 * skipped by quic_sock_accept_conn().
 	 */
 	BUG_ON(qc->flags & (QUIC_FL_CONN_CLOSING|QUIC_FL_CONN_DRAINING));