diff --git a/src/backend/postmaster/postmaster.c b/src/backend/postmaster/postmaster.c
index 5d09822c81..3dd0a022f7 100644
--- a/src/backend/postmaster/postmaster.c
+++ b/src/backend/postmaster/postmaster.c
@@ -2887,6 +2887,8 @@ pmdie(SIGNAL_ARGS)
 			sd_notify(0, "STOPPING=1");
 #endif
 
+			/* tell children to shut down ASAP */
+			SetQuitSignalReason(PMQUIT_FOR_STOP);
 			TerminateChildren(SIGQUIT);
 			pmState = PM_WAIT_BACKENDS;
 
@@ -3464,6 +3466,7 @@ HandleChildCrash(int pid, int exitstatus, const char *procname)
 		LogChildExit(LOG, procname, pid, exitstatus);
 		ereport(LOG,
 				(errmsg("terminating any other active server processes")));
+		SetQuitSignalReason(PMQUIT_FOR_CRASH);
 	}
 
 	/* Process background workers. */
diff --git a/src/backend/storage/ipc/pmsignal.c b/src/backend/storage/ipc/pmsignal.c
index 94c65877c1..8ef3f6da4a 100644
--- a/src/backend/storage/ipc/pmsignal.c
+++ b/src/backend/storage/ipc/pmsignal.c
@@ -1,7 +1,7 @@
 /*-------------------------------------------------------------------------
  *
  * pmsignal.c
- *	  routines for signaling the postmaster from its child processes
+ *	  routines for signaling between the postmaster and its child processes
  *
  *
  * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group
@@ -55,6 +55,10 @@
  * but carries the extra information that the child is a WAL sender.
  * WAL senders too start in ACTIVE state, but switch to WALSENDER once they
  * start streaming the WAL (and they never go back to ACTIVE after that).
+ *
+ * We also have a shared-memory field that is used for communication in
+ * the opposite direction, from postmaster to children: it tells why the
+ * postmaster has broadcasted SIGQUIT signals, if indeed it has done so.
  */
 
 #define PM_CHILD_UNUSED		0	/* these values must fit in sig_atomic_t */
@@ -65,8 +69,10 @@
 /* "typedef struct PMSignalData PMSignalData" appears in pmsignal.h */
 struct PMSignalData
 {
-	/* per-reason flags */
+	/* per-reason flags for signaling the postmaster */
 	sig_atomic_t PMSignalFlags[NUM_PMSIGNALS];
+	/* global flags for signals from postmaster to children */
+	QuitSignalReason sigquit_reason;	/* why SIGQUIT was sent */
 	/* per-child-process flags */
 	int			num_child_flags;	/* # of entries in PMChildFlags[] */
 	int			next_child_flag;	/* next slot to try to assign */
@@ -134,6 +140,7 @@ PMSignalShmemInit(void)
 
 	if (!found)
 	{
+		/* initialize all flags to zeroes */
 		MemSet(unvolatize(PMSignalData *, PMSignalState), 0, PMSignalShmemSize());
 		PMSignalState->num_child_flags = MaxLivePostmasterChildren();
 	}
@@ -171,6 +178,34 @@ CheckPostmasterSignal(PMSignalReason reason)
 	return false;
 }
 
+/*
+ * SetQuitSignalReason - broadcast the reason for a system shutdown.
+ * Should be called by postmaster before sending SIGQUIT to children.
+ *
+ * Note: in a crash-and-restart scenario, the "reason" field gets cleared
+ * as a part of rebuilding shared memory; the postmaster need not do it
+ * explicitly.
+ */
+void
+SetQuitSignalReason(QuitSignalReason reason)
+{
+	PMSignalState->sigquit_reason = reason;
+}
+
+/*
+ * GetQuitSignalReason - obtain the reason for a system shutdown.
+ * Called by child processes when they receive SIGQUIT.
+ * If the postmaster hasn't actually sent SIGQUIT, will return PMQUIT_NOT_SENT.
+ */
+QuitSignalReason
+GetQuitSignalReason(void)
+{
+	/* This is called in signal handlers, so be extra paranoid. */
+	if (!IsUnderPostmaster || PMSignalState == NULL)
+		return PMQUIT_NOT_SENT;
+	return PMSignalState->sigquit_reason;
+}
+
 
 /*
  * AssignPostmasterChildSlot - select an unused slot for a new postmaster
diff --git a/src/backend/tcop/postgres.c b/src/backend/tcop/postgres.c
index 3679799e50..c3c0a0c01d 100644
--- a/src/backend/tcop/postgres.c
+++ b/src/backend/tcop/postgres.c
@@ -67,6 +67,7 @@
 #include "rewrite/rewriteHandler.h"
 #include "storage/bufmgr.h"
 #include "storage/ipc.h"
+#include "storage/pmsignal.h"
 #include "storage/proc.h"
 #include "storage/procsignal.h"
 #include "storage/sinval.h"
@@ -2752,8 +2753,8 @@ drop_unnamed_stmt(void)
 /*
  * quickdie() occurs when signaled SIGQUIT by the postmaster.
  *
- * Some backend has bought the farm,
- * so we need to stop what we're doing and exit.
+ * Either some backend has bought the farm, or we've been told to shut down
+ * "immediately"; so we need to stop what we're doing and exit.
  */
 void
 quickdie(SIGNAL_ARGS)
@@ -2788,18 +2789,36 @@ quickdie(SIGNAL_ARGS)
 	 * wrong, so there's not much to lose.  Assuming the postmaster is still
 	 * running, it will SIGKILL us soon if we get stuck for some reason.
 	 *
-	 * Ideally this should be ereport(FATAL), but then we'd not get control
-	 * back...
+	 * Ideally these should be ereport(FATAL), but then we'd not get control
+	 * back to force the correct type of process exit.
 	 */
-	ereport(WARNING,
-			(errcode(ERRCODE_CRASH_SHUTDOWN),
-			 errmsg("terminating connection because of crash of another server process"),
-			 errdetail("The postmaster has commanded this server process to roll back"
-					   " the current transaction and exit, because another"
-					   " server process exited abnormally and possibly corrupted"
-					   " shared memory."),
-			 errhint("In a moment you should be able to reconnect to the"
-					 " database and repeat your command.")));
+	switch (GetQuitSignalReason())
+	{
+		case PMQUIT_NOT_SENT:
+			/* Hmm, SIGQUIT arrived out of the blue */
+			ereport(WARNING,
+					(errcode(ERRCODE_ADMIN_SHUTDOWN),
+					 errmsg("terminating connection because of unexpected SIGQUIT signal")));
+			break;
+		case PMQUIT_FOR_CRASH:
+			/* A crash-and-restart cycle is in progress */
+			ereport(WARNING,
+					(errcode(ERRCODE_CRASH_SHUTDOWN),
+					 errmsg("terminating connection because of crash of another server process"),
+					 errdetail("The postmaster has commanded this server process to roll back"
+							   " the current transaction and exit, because another"
+							   " server process exited abnormally and possibly corrupted"
+							   " shared memory."),
+					 errhint("In a moment you should be able to reconnect to the"
+							 " database and repeat your command.")));
+			break;
+		case PMQUIT_FOR_STOP:
+			/* Immediate-mode stop */
+			ereport(WARNING,
+					(errcode(ERRCODE_ADMIN_SHUTDOWN),
+					 errmsg("terminating connection due to administrator command")));
+			break;
+	}
 
 	/*
 	 * We DO NOT want to run proc_exit() or atexit() callbacks -- we're here
diff --git a/src/include/storage/pmsignal.h b/src/include/storage/pmsignal.h
index 56c5ec4481..b6aa158160 100644
--- a/src/include/storage/pmsignal.h
+++ b/src/include/storage/pmsignal.h
@@ -1,7 +1,7 @@
 /*-------------------------------------------------------------------------
  *
  * pmsignal.h
- *	  routines for signaling the postmaster from its child processes
+ *	  routines for signaling between the postmaster and its child processes
  *
  *
  * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group
@@ -45,6 +45,16 @@ typedef enum
 	NUM_PMSIGNALS				/* Must be last value of enum! */
 } PMSignalReason;
 
+/*
+ * Reasons why the postmaster would send SIGQUIT to its children.
+ */
+typedef enum
+{
+	PMQUIT_NOT_SENT = 0,		/* postmaster hasn't sent SIGQUIT */
+	PMQUIT_FOR_CRASH,			/* some other backend bought the farm */
+	PMQUIT_FOR_STOP				/* immediate stop was commanded */
+} QuitSignalReason;
+
 /* PMSignalData is an opaque struct, details known only within pmsignal.c */
 typedef struct PMSignalData PMSignalData;
 
@@ -55,6 +65,8 @@ extern Size PMSignalShmemSize(void);
 extern void PMSignalShmemInit(void);
 extern void SendPostmasterSignal(PMSignalReason reason);
 extern bool CheckPostmasterSignal(PMSignalReason reason);
+extern void SetQuitSignalReason(QuitSignalReason reason);
+extern QuitSignalReason GetQuitSignalReason(void);
 extern int	AssignPostmasterChildSlot(void);
 extern bool ReleasePostmasterChildSlot(int slot);
 extern bool IsPostmasterChildWalSender(int slot);