diff --git a/testcases/complete-run.pl.in b/testcases/complete-run.pl.in
index ba192469..ddd6ccad 100755
--- a/testcases/complete-run.pl.in
+++ b/testcases/complete-run.pl.in
@@ -177,11 +177,18 @@ my $timingsjson = slurp('.last_run_timings.json') if -e '.last_run_timings.json'
              map  { [$_, $timings{$_} // 999] } @testfiles;
 
 # Run 000-load-deps.t first to bail out early when dependencies are missing.
-my $loadtest = "t/000-load-deps.t";
-if ((scalar grep { $_ eq $loadtest } @testfiles) > 0) {
+my ($loadtest) = grep { $_ =~ m,t/000-load-deps.t$, } @testfiles;
+if (defined($loadtest)) {
     @testfiles = ($loadtest, grep { $_ ne $loadtest } @testfiles);
 }
 
+# Run 533-randr15.t last because it destructively modifies the RandR
+# configuration of the X session, interfering with any test started afterwards.
+my ($randrtest) = grep { $_ =~ m,t/533-randr15.t$, } @testfiles;
+if (defined($randrtest)) {
+    @testfiles = ((grep { $_ ne $randrtest } @testfiles), $randrtest);
+}
+
 printf("\nRough time estimate for this run: %.2f seconds\n\n", $timings{GLOBAL})
     if exists($timings{GLOBAL});
 
diff --git a/testcases/lib/TestWorker.pm b/testcases/lib/TestWorker.pm
index aee994f7..c56767c4 100644
--- a/testcases/lib/TestWorker.pm
+++ b/testcases/lib/TestWorker.pm
@@ -99,6 +99,11 @@ sub worker_wait {
 
             $0 = $file;
 
+            # Re-seed rand() so that File::Temp’s tempnam produces different
+            # results, making a TOCTOU between e.g. t/175-startup-notification.t
+            # and t/180-fd-leaks.t less likely.
+            srand(time ^ $$);
+
             POSIX::dup2($ipc_fd, 0);
             POSIX::dup2($ipc_fd, 1);
             POSIX::dup2(1, 2);
diff --git a/testcases/t/263-edge-borders.t b/testcases/t/263-edge-borders.t
index 0d14c65c..6da1dacd 100644
--- a/testcases/t/263-edge-borders.t
+++ b/testcases/t/263-edge-borders.t
@@ -147,6 +147,10 @@ ok(@{get_ws_content($tmp)} == 2, 'after split & new window, two containers');
 
 $wscontent = get_ws($tmp);
 
+# Ensure i3’s X11 requests are processed before our inquiry via
+# $tilewindow->rect:
+sync_with_i3;
+
 @tiled = @{$wscontent->{nodes}};
 ok(@tiled == 2, 'two tiled container opened in another container');
 is($tiled[0]->{current_border_width}, -1, 'first tiled current border width set to -1');