diff --git a/src/backend/postmaster/postmaster.c b/src/backend/postmaster/postmaster.c
index e0a15e9f099..ee531868c8d 100644
--- a/src/backend/postmaster/postmaster.c
+++ b/src/backend/postmaster/postmaster.c
@@ -400,6 +400,7 @@ static void processCancelRequest(Port *port, void *pkt);
 static int	initMasks(fd_set *rmask);
 static void report_fork_failure_to_client(Port *port, int errnum);
 static CAC_state canAcceptConnections(void);
+static long PostmasterRandom(void);
 static void RandomSalt(char *md5Salt);
 static void signal_child(pid_t pid, int signal);
 static bool SignalSomeChildren(int signal, int targets);
@@ -559,6 +560,16 @@ PostmasterMain(int argc, char *argv[])
 	 */
 	umask(S_IRWXG | S_IRWXO);
 
+	/*
+	 * Initialize random(3) so we don't get the same values in every run.
+	 *
+	 * Note: the seed is pretty predictable from externally-visible facts such
+	 * as postmaster start time, so avoid using random() for security-critical
+	 * random values during postmaster startup.  At the time of first
+	 * connection, PostmasterRandom will select a hopefully-more-random seed.
+	 */
+	srandom((unsigned int) (MyProcPid ^ MyStartTime));
+
 	/*
 	 * By default, palloc() requests in the postmaster will be allocated in
 	 * the PostmasterContext, which is space that can be recycled by backends.
@@ -5125,8 +5136,12 @@ RandomSalt(char *md5Salt)
 
 /*
  * PostmasterRandom
+ *
+ * Caution: use this only for values needed during connection-request
+ * processing.  Otherwise, the intended property of having an unpredictable
+ * delay between random_start_time and random_stop_time will be broken.
  */
-long
+static long
 PostmasterRandom(void)
 {
 	/*
diff --git a/src/backend/storage/ipc/dsm.c b/src/backend/storage/ipc/dsm.c
index 357e8a98e54..7ce45caaf9b 100644
--- a/src/backend/storage/ipc/dsm.c
+++ b/src/backend/storage/ipc/dsm.c
@@ -36,7 +36,6 @@
 
 #include "lib/ilist.h"
 #include "miscadmin.h"
-#include "postmaster/postmaster.h"
 #include "storage/dsm.h"
 #include "storage/ipc.h"
 #include "storage/lwlock.h"
@@ -180,7 +179,7 @@ dsm_postmaster_startup(PGShmemHeader *shim)
 	{
 		Assert(dsm_control_address == NULL);
 		Assert(dsm_control_mapped_size == 0);
-		dsm_control_handle = (dsm_handle) PostmasterRandom();
+		dsm_control_handle = random();
 		if (dsm_control_handle == 0)
 			continue;
 		if (dsm_impl_op(DSM_OP_CREATE, dsm_control_handle, segsize,
diff --git a/src/include/postmaster/postmaster.h b/src/include/postmaster/postmaster.h
index 9cf9e5a61d2..de463327806 100644
--- a/src/include/postmaster/postmaster.h
+++ b/src/include/postmaster/postmaster.h
@@ -48,7 +48,6 @@ extern const char *progname;
 
 extern void PostmasterMain(int argc, char *argv[]) __attribute__((noreturn));
 extern void ClosePostmasterPorts(bool am_syslogger);
-extern long PostmasterRandom(void);
 
 extern int	MaxLivePostmasterChildren(void);