diff --git a/src/backend/postmaster/postmaster.c b/src/backend/postmaster/postmaster.c
index 60d29a2089a..0edd7f1dc7f 100644
--- a/src/backend/postmaster/postmaster.c
+++ b/src/backend/postmaster/postmaster.c
@@ -3811,12 +3811,8 @@ PostmasterStateMachine(void)
 		 * dead_end children left. There shouldn't be any regular backends
 		 * left by now anyway; what we're really waiting for is walsenders and
 		 * archiver.
-		 *
-		 * Walreceiver should normally be dead by now, but not when a fast
-		 * shutdown is performed during recovery.
 		 */
-		if (PgArchPID == 0 && CountChildren(BACKEND_TYPE_ALL) == 0 &&
-			WalReceiverPID == 0)
+		if (PgArchPID == 0 && CountChildren(BACKEND_TYPE_ALL) == 0)
 		{
 			pmState = PM_WAIT_DEAD_END;
 		}
@@ -5213,16 +5209,25 @@ sigusr1_handler(SIGNAL_ARGS)
 		MaybeStartWalReceiver();
 	}
 
-	if (CheckPostmasterSignal(PMSIGNAL_ADVANCE_STATE_MACHINE) &&
-		(pmState == PM_WAIT_BACKUP || pmState == PM_WAIT_BACKENDS))
+	/*
+	 * Try to advance postmaster's state machine, if a child requests it.
+	 *
+	 * Be careful about the order of this action relative to sigusr1_handler's
+	 * other actions.  Generally, this should be after other actions, in case
+	 * they have effects PostmasterStateMachine would need to know about.
+	 * However, we should do it before the CheckPromoteSignal step, which
+	 * cannot have any (immediate) effect on the state machine, but does
+	 * depend on what state we're in now.
+	 */
+	if (CheckPostmasterSignal(PMSIGNAL_ADVANCE_STATE_MACHINE))
 	{
-		/* Advance postmaster's state machine */
 		PostmasterStateMachine();
 	}
 
-	if (CheckPromoteSignal() && StartupPID != 0 &&
+	if (StartupPID != 0 &&
 		(pmState == PM_STARTUP || pmState == PM_RECOVERY ||
-		 pmState == PM_HOT_STANDBY || pmState == PM_WAIT_READONLY))
+		 pmState == PM_HOT_STANDBY || pmState == PM_WAIT_READONLY) &&
+		CheckPromoteSignal())
 	{
 		/* Tell startup process to finish recovery */
 		signal_child(StartupPID, SIGUSR2);
@@ -5518,6 +5523,14 @@ StartAutovacuumWorker(void)
 /*
  * MaybeStartWalReceiver
  *		Start the WAL receiver process, if not running and our state allows.
+ *
+ * Note: if WalReceiverPID is already nonzero, it might seem that we should
+ * clear WalReceiverRequested.  However, there's a race condition if the
+ * walreceiver terminates and the startup process immediately requests a new
+ * one: it's quite possible to get the signal for the request before reaping
+ * the dead walreceiver process.  Better to risk launching an extra
+ * walreceiver than to miss launching one we need.  (The walreceiver code
+ * has logic to recognize that it should go away if not needed.)
  */
 static void
 MaybeStartWalReceiver(void)
@@ -5528,7 +5541,9 @@ MaybeStartWalReceiver(void)
 		Shutdown == NoShutdown)
 	{
 		WalReceiverPID = StartWalReceiver();
-		WalReceiverRequested = false;
+		if (WalReceiverPID != 0)
+			WalReceiverRequested = false;
+		/* else leave the flag set, so we'll try again later */
 	}
 }