diff --git a/contrib/pg_prewarm/autoprewarm.c b/contrib/pg_prewarm/autoprewarm.c
index edec1dfd0b..1701da9dff 100644
--- a/contrib/pg_prewarm/autoprewarm.c
+++ b/contrib/pg_prewarm/autoprewarm.c
@@ -400,12 +400,7 @@ apw_load_buffers(void)
 
 		/*
 		 * Likewise, don't launch if we've already been told to shut down.
-		 *
-		 * There is a race condition here: if the postmaster has received a
-		 * fast-shutdown signal, but we've not heard about it yet, then the
-		 * postmaster will ignore our worker start request and we'll wait
-		 * forever.  However, that's a bug in the general background-worker
-		 * logic, not the fault of this module.
+		 * (The launch would fail anyway, but we might as well skip it.)
 		 */
 		if (got_sigterm)
 			break;
diff --git a/src/backend/postmaster/bgworker.c b/src/backend/postmaster/bgworker.c
index d043ced686..4a5c0e5509 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 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 we aren't allowing new workers, then immediately mark it for
+		 * termination; the next stanza will take care of cleaning it up.
+		 * Doing this ensures that any process waiting for the worker will get
+		 * awoken, even though the worker will never be allowed to run.
+		 */
+		if (!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 +514,55 @@ BackgroundWorkerStopNotifications(pid_t pid)
 	}
 }
 
+/*
+ * Cancel any not-yet-started worker requests that have waiting processes.
+ *
+ * This is called during a normal ("smart" or "fast") database shutdown.
+ * After this point, no new background workers will be started, so anything
+ * that might be waiting for them needs to be kicked off its wait.  We do
+ * that by cancelling the bgworker registration entirely, which is perhaps
+ * overkill, but since we're shutting down it does not matter whether the
+ * registration record sticks around.
+ *
+ * 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 there's someone waiting ... */
+		if (slot->pid == InvalidPid &&
+			rw->rw_worker.bgw_notify_pid != 0)
+		{
+			/* ... then zap it, and notify the waiter */
+			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 immediately, since we won't ever restart them.
+ *
+ * This function should only be called from the postmaster.
  */
 void
 ResetBackgroundWorkerCrashTimes(void)
@@ -548,6 +602,11 @@ ResetBackgroundWorkerCrashTimes(void)
 			 * resetting.
 			 */
 			rw->rw_crashed_at = 0;
+
+			/*
+			 * If there was anyone waiting for it, they're history.
+			 */
+			rw->rw_worker.bgw_notify_pid = 0;
 		}
 	}
 }
@@ -1077,6 +1136,9 @@ GetBackgroundWorkerPid(BackgroundWorkerHandle *handle, pid_t *pidp)
  * returned.  However, if the postmaster has died, we give up and return
  * BGWH_POSTMASTER_DIED, since it that case we know that startup will not
  * take place.
+ *
+ * The caller *must* have set our PID as the worker's bgw_notify_pid,
+ * else we will not be awoken promptly when the worker's state changes.
  */
 BgwHandleStatus
 WaitForBackgroundWorkerStartup(BackgroundWorkerHandle *handle, pid_t *pidp)
@@ -1119,6 +1181,9 @@ WaitForBackgroundWorkerStartup(BackgroundWorkerHandle *handle, pid_t *pidp)
  * and then return BGWH_STOPPED.  However, if the postmaster has died, we give
  * up and return BGWH_POSTMASTER_DIED, because it's the postmaster that
  * notifies us when a worker's state changes.
+ *
+ * The caller *must* have set our PID as the worker's bgw_notify_pid,
+ * else we will not be awoken promptly when the worker's state changes.
  */
 BgwHandleStatus
 WaitForBackgroundWorkerShutdown(BackgroundWorkerHandle *handle)
diff --git a/src/backend/postmaster/postmaster.c b/src/backend/postmaster/postmaster.c
index 851d9ddb12..b39413c685 100644
--- a/src/backend/postmaster/postmaster.c
+++ b/src/backend/postmaster/postmaster.c
@@ -3804,6 +3804,13 @@ PostmasterStateMachine(void)
 	 */
 	if (pmState == PM_STOP_BACKENDS)
 	{
+		/*
+		 * Forget any pending requests for 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);
@@ -5194,13 +5201,6 @@ sigusr1_handler(SIGNAL_ARGS)
 	PG_SETMASK(&BlockSig);
 #endif
 
-	/* Process background worker state change. */
-	if (CheckPostmasterSignal(PMSIGNAL_BACKGROUND_WORKER_CHANGE))
-	{
-		BackgroundWorkerStateChange();
-		StartWorkerNeeded = true;
-	}
-
 	/*
 	 * RECOVERY_STARTED and BEGIN_HOT_STANDBY signals are ignored in
 	 * unexpected states. If the startup process quickly starts up, completes
@@ -5246,6 +5246,7 @@ sigusr1_handler(SIGNAL_ARGS)
 
 		pmState = PM_RECOVERY;
 	}
+
 	if (CheckPostmasterSignal(PMSIGNAL_BEGIN_HOT_STANDBY) &&
 		pmState == PM_RECOVERY && Shutdown == NoShutdown)
 	{
@@ -5271,6 +5272,14 @@ sigusr1_handler(SIGNAL_ARGS)
 		StartWorkerNeeded = true;
 	}
 
+	/* Process background worker state changes. */
+	if (CheckPostmasterSignal(PMSIGNAL_BACKGROUND_WORKER_CHANGE))
+	{
+		/* Accept new worker requests only if not stopping. */
+		BackgroundWorkerStateChange(pmState < PM_STOP_BACKENDS);
+		StartWorkerNeeded = true;
+	}
+
 	if (StartWorkerNeeded || HaveCrashedWorker)
 		maybe_start_bgworkers();
 
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 */