diff --git a/kernel/sched/ext/ext.c b/kernel/sched/ext/ext.c
index ac8fe70a9fb6..64d937fb2b24 100644
--- a/kernel/sched/ext/ext.c
+++ b/kernel/sched/ext/ext.c
@@ -3213,8 +3213,7 @@ static void put_prev_task_scx(struct rq *rq, struct task_struct *p,
 		/*
 		 * If @p is runnable but we're about to enter a lower
 		 * sched_class, %SCX_OPS_ENQ_LAST must be set. Tell
-		 * ops.enqueue() that @p is the only one available for this cpu,
-		 * which should trigger an explicit follow-up scheduling event.
+		 * ops.enqueue() that @p is the only one available for this cpu.
 		 * This doesn't apply if the baseline access on the CPU is lost.
 		 *
 		 * Under core scheduling, a pick dispatches only when nothing is
@@ -3226,6 +3225,16 @@ static void put_prev_task_scx(struct rq *rq, struct task_struct *p,
 			WARN_ON_ONCE(!sched_core_enabled(rq) &&
 				     !(sch->ops.flags & SCX_OPS_ENQ_LAST));
 			scx_do_enqueue_task(rq, p, SCX_ENQ_LAST, -1);
+
+			/*
+			 * A task put on the local DSQ runs, as anywhere else.
+			 * Here the insert can't reschedule on its own: the pick
+			 * has settled on @next and @p is still curr, so
+			 * resched_curr() would flag @p and __schedule() clears
+			 * that right after the pick. Flag @next instead.
+			 */
+			if (p->scx.dsq == &rq->scx.local_dsq)
+				set_tsk_need_resched(next);
 		} else {
 			scx_do_enqueue_task(rq, p, 0, -1);
 		}
diff --git a/kernel/sched/ext/internal.h b/kernel/sched/ext/internal.h
index 5b37faa532d6..85579fcabf52 100644
--- a/kernel/sched/ext/internal.h
+++ b/kernel/sched/ext/internal.h
@@ -1774,8 +1774,9 @@ enum scx_enq_flags {
 	 * %SCX_OPS_ENQ_LAST is specified, they're ops.enqueue()'d with the
 	 * %SCX_ENQ_LAST flag set.
 	 *
-	 * The BPF scheduler is responsible for triggering a follow-up
-	 * scheduling event. Otherwise, Execution may stall.
+	 * If the task is queued on the local DSQ of the CPU it was running on,
+	 * it continues to run. Otherwise, the CPU goes idle. A scheduler that
+	 * wants a full dispatch cycle on the CPU should kick it.
 	 */
 	SCX_ENQ_LAST		= 1LLU << 41,