diff --git a/src/test/modules/test_checksums/t/006_concurrent_pgbench.pl b/src/test/modules/test_checksums/t/006_concurrent_pgbench.pl
index b33ca6e0c26..5cee6d4a6b5 100644
--- a/src/test/modules/test_checksums/t/006_concurrent_pgbench.pl
+++ b/src/test/modules/test_checksums/t/006_concurrent_pgbench.pl
@@ -55,7 +55,7 @@ if ($ENV{enable_injection_points} ne 'yes')
 # whether to turn things off during testing.
 sub cointoss
 {
-	return int(rand(2) == 1);
+	return int(rand() < 0.5);
 }
 
 # Helper for injecting random sleeps here and there in the testrun. The sleep
@@ -74,7 +74,7 @@ sub background_ro_pgbench
 	my ($port, $stdin, $stdout, $stderr) = @_;
 
 	my $pgbench_primary = IPC::Run::start(
-		[ 'pgbench', '-p', $port, '-S', '-T', '600', '-c', '10', 'postgres' ],
+		[ 'pgbench', '-n', '-p', $port, '-S', '-T', '600', '-c', '10', 'postgres' ],
 		'<' => \$stdin,
 		'>' => \$stdout,
 		'2>' => \$stderr,
@@ -224,6 +224,9 @@ background_rw_pgbench(
 	$node_primary->port, $pgb_primary_stdin,
 	$pgb_primary_stdout, $pgb_primary_stderr);
 
+my $primary_shutdown_clean = 0;
+my $standby_shutdown_clean = 0;
+
 # Main test suite. This loop will start a pgbench run on the cluster and while
 # that's running flip the state of data checksums concurrently. It will then
 # randomly restart thec cluster (in fast or immediate) mode and then check for
@@ -246,9 +249,11 @@ for (my $i = 0; $i < $TEST_ITERATIONS; $i++)
 		$node_primary_loglocation = -s $node_primary->logfile;
 
 		# If data checksums are enabled, take the opportunity to verify them
-		# while the cluster is offline
+		# while the cluster is offline (but only if stopped in a clean way,
+		# not after immediate shutdown)
 		$node_primary->checksum_verify_offline()
-		  unless $data_checksum_state eq 'off';
+		  unless $data_checksum_state eq 'off' or !$primary_shutdown_clean;
+
 		random_sleep();
 		$node_primary->start;
 		# Start a pgbench in the background against the primary
@@ -270,9 +275,11 @@ for (my $i = 0; $i < $TEST_ITERATIONS; $i++)
 		$node_standby_1_loglocation = -s $node_standby_1->logfile;
 
 		# If data checksums are enabled, take the opportunity to verify them
-		# while the cluster is offline
+		# while the cluster is offline (but only if stopped in a clean way,
+		# not after immediate shutdown)
 		$node_standby_1->checksum_verify_offline()
-		  unless $data_checksum_state eq 'off';
+		  unless $data_checksum_state eq 'off' or !$standby_shutdown_clean;
+
 		random_sleep();
 		$node_standby_1->start;
 		# Start a select-only pgbench in the background on the standby
@@ -287,13 +294,41 @@ for (my $i = 0; $i < $TEST_ITERATIONS; $i++)
 	my $result = $node_primary->safe_psql('postgres',
 		"SELECT count(*) FROM t WHERE a > 1");
 	is($result, '100000', 'ensure data pages can be read back on primary');
+
 	random_sleep();
+
 	$node_primary->wait_for_catchup($node_standby_1, 'write');
 
-	# Potentially powercycle the cluster
-	$node_primary->stop($stop_modes[ int(rand(100)) ]) if cointoss();
 	random_sleep();
-	$node_standby_1->stop($stop_modes[ int(rand(100)) ]) if cointoss();
+
+	# Potentially powercycle the cluster (the nodes independently)
+	# XXX should maybe try stopping nodes in the opposite order too?
+	if (cointoss())
+	{
+		my $mode = $stop_modes[ int(rand(100)) ];
+		$node_primary->stop($mode);
+		$primary_shutdown_clean = ($mode eq 'fast');
+	}
+
+	random_sleep();
+
+	if (cointoss())
+	{
+		my $mode = $stop_modes[ int(rand(100)) ];
+		$node_standby_1->stop($mode);
+		$standby_shutdown_clean = ($mode eq 'fast');
+	}
+}
+
+# make sure the nodes are running
+if (!$node_primary->is_alive)
+{
+	$node_primary->start;
+}
+
+if (!$node_standby_1->is_alive)
+{
+        $node_standby_1->start;
 }
 
 # Testrun is over, ensure that data reads back as expected and perform a final