diff --git a/src/backend/postmaster/bgworker.c b/src/backend/postmaster/bgworker.c
index 7ef6259eb5..b3ab8b0fa3 100644
--- a/src/backend/postmaster/bgworker.c
+++ b/src/backend/postmaster/bgworker.c
@@ -231,13 +231,15 @@ FindRegisteredWorkerBySlotNumber(int slotno)
 }
 
 /*
- * Notice changes to shared memory made by other backends.  This code
- * runs in the postmaster, so we must be very careful not to assume that
- * shared memory contents are sane.  Otherwise, a rogue backend could take
- * out the postmaster.
+ * Notice changes to shared memory made by other backends.
+ * Accept new dynamic worker requests only if allow_new_workers is true.
+ *
+ * This code runs in the postmaster, so we must be very careful not to assume
+ * that shared memory contents are sane.  Otherwise, a rogue backend could
+ * take out the postmaster.
  */
 void
-BackgroundWorkerStateChange(void)
+BackgroundWorkerStateChange(bool allow_new_workers)
 {
 	int			slotno;
 
@@ -297,6 +299,15 @@ BackgroundWorkerStateChange(void)
 			continue;
 		}
 
+		/*
+		 * If this is a dynamic worker request, and we aren't allowing new
+		 * dynamic workers, then immediately mark it for termination; the next
+		 * stanza will take care of cleaning it up.
+		 */
+		if (slot->worker.bgw_restart_time == BGW_NEVER_RESTART &&
+			!allow_new_workers)
+			slot->terminate = true;
+
 		/*
 		 * If the worker is marked for termination, we don't need to add it to
 		 * the registered workers list; we can just free the slot. However, if
@@ -503,12 +514,54 @@ BackgroundWorkerStopNotifications(pid_t pid)
 	}
 }
 
+/*
+ * Cancel any not-yet-started worker requests that have BGW_NEVER_RESTART.
+ *
+ * This is called during a normal ("smart" or "fast") database shutdown.
+ * After this point, no new background workers will be started, so any
+ * dynamic worker requests should be killed off, allowing anything that
+ * might be waiting for them to clean up and exit.
+ *
+ * This function should only be called from the postmaster.
+ */
+void
+ForgetUnstartedBackgroundWorkers(void)
+{
+	slist_mutable_iter iter;
+
+	slist_foreach_modify(iter, &BackgroundWorkerList)
+	{
+		RegisteredBgWorker *rw;
+		BackgroundWorkerSlot *slot;
+
+		rw = slist_container(RegisteredBgWorker, rw_lnode, iter.cur);
+		Assert(rw->rw_shmem_slot < max_worker_processes);
+		slot = &BackgroundWorkerData->slot[rw->rw_shmem_slot];
+
+		/* If it's not yet started, and it's a dynamic worker ... */
+		if (slot->pid == InvalidPid &&
+			rw->rw_worker.bgw_restart_time == BGW_NEVER_RESTART)
+		{
+			/* ... then zap it, and notify anything that was waiting */
+			int			notify_pid = rw->rw_worker.bgw_notify_pid;
+
+			ForgetBackgroundWorker(&iter);
+			if (notify_pid != 0)
+				kill(notify_pid, SIGUSR1);
+		}
+	}
+}
+
 /*
  * Reset background worker crash state.
  *
  * We assume that, after a crash-and-restart cycle, background workers without
  * the never-restart flag should be restarted immediately, instead of waiting
- * for bgw_restart_time to elapse.
+ * for bgw_restart_time to elapse.  On the other hand, workers with that flag
+ * should be forgotten, because they are dynamic requests from processes that
+ * no longer exist.
+ *
+ * This function should only be called from the postmaster.
  */
 void
 ResetBackgroundWorkerCrashTimes(void)
diff --git a/src/backend/postmaster/postmaster.c b/src/backend/postmaster/postmaster.c
index 5d09822c81..fa35bf4369 100644
--- a/src/backend/postmaster/postmaster.c
+++ b/src/backend/postmaster/postmaster.c
@@ -3796,6 +3796,13 @@ PostmasterStateMachine(void)
 	 */
 	if (pmState == PM_STOP_BACKENDS)
 	{
+		/*
+		 * Forget any pending requests for dynamic background workers, since
+		 * we're no longer willing to launch any new workers.  (If additional
+		 * requests arrive, BackgroundWorkerStateChange will reject them.)
+		 */
+		ForgetUnstartedBackgroundWorkers();
+
 		/* Signal all backend children except walsenders */
 		SignalSomeChildren(SIGTERM,
 						   BACKEND_TYPE_ALL - BACKEND_TYPE_WALSND);
@@ -5153,7 +5160,8 @@ sigusr1_handler(SIGNAL_ARGS)
 	/* Process background worker state change. */
 	if (CheckPostmasterSignal(PMSIGNAL_BACKGROUND_WORKER_CHANGE))
 	{
-		BackgroundWorkerStateChange();
+		/* Accept new dynamic worker requests only if not stopping. */
+		BackgroundWorkerStateChange(pmState < PM_STOP_BACKENDS);
 		StartWorkerNeeded = true;
 	}
 
diff --git a/src/include/postmaster/bgworker_internals.h b/src/include/postmaster/bgworker_internals.h
index f7e24664d5..dd6cabc45b 100644
--- a/src/include/postmaster/bgworker_internals.h
+++ b/src/include/postmaster/bgworker_internals.h
@@ -46,11 +46,12 @@ extern slist_head BackgroundWorkerList;
 
 extern Size BackgroundWorkerShmemSize(void);
 extern void BackgroundWorkerShmemInit(void);
-extern void BackgroundWorkerStateChange(void);
+extern void BackgroundWorkerStateChange(bool allow_new_workers);
 extern void ForgetBackgroundWorker(slist_mutable_iter *cur);
 extern void ReportBackgroundWorkerPID(RegisteredBgWorker *);
 extern void ReportBackgroundWorkerExit(slist_mutable_iter *cur);
 extern void BackgroundWorkerStopNotifications(pid_t pid);
+extern void ForgetUnstartedBackgroundWorkers(void);
 extern void ResetBackgroundWorkerCrashTimes(void);
 
 /* Function to start a background worker, called from postmaster.c */