diff --git a/src/backend/postmaster/postmaster.c b/src/backend/postmaster/postmaster.c
index 41de140ae01..b50776678f7 100644
--- a/src/backend/postmaster/postmaster.c
+++ b/src/backend/postmaster/postmaster.c
@@ -602,8 +602,8 @@ PostmasterMain(int argc, char *argv[])
 	 *
 	 * 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.
+	 * random values during postmaster startup.  InitPostmasterChild() will
+	 * set a new seed in child processes.
 	 */
 	srandom((unsigned int) (MyProcPid ^ MyStartTime));
 
@@ -4315,22 +4315,16 @@ BackendRun(Port *port)
 	char	  **av;
 	int			maxac;
 	int			ac;
-	long		secs;
-	int			usecs;
 	int			i;
 
 	/*
 	 * Don't want backend to be able to see the postmaster random number
-	 * generator state.  We have to clobber the static random_seed *and* start
-	 * a new random sequence in the random() library function.
+	 * generator state.  We have to clobber the static random_seed.
 	 */
 #ifndef HAVE_STRONG_RANDOM
 	random_seed = 0;
 	random_start_time.tv_usec = 0;
 #endif
-	/* slightly hacky way to convert timestamptz into integers */
-	TimestampDifference(0, port->SessionStartTime, &secs, &usecs);
-	srandom((unsigned int) (MyProcPid ^ (usecs << 12) ^ secs));
 
 	/*
 	 * Now, build the argv vector that will be given to PostgresMain.
diff --git a/src/backend/utils/init/miscinit.c b/src/backend/utils/init/miscinit.c
index f590ecb25e8..d907226ada4 100644
--- a/src/backend/utils/init/miscinit.c
+++ b/src/backend/utils/init/miscinit.c
@@ -278,6 +278,9 @@ InitPostmasterChild(void)
 
 	MyStartTime = time(NULL);	/* set our start time in case we call elog */
 
+	/* Set a different seed for libc's random() in every backend. */
+	srandom((unsigned int) (MyProcPid ^ MyStartTime));
+
 	/*
 	 * make sure stderr is in binary mode before anything can possibly be
 	 * written to it, in case it's actually the syslogger pipe, so the pipe