diff --git a/tests/checks/jobs.fish b/tests/checks/jobs.fish
index 3b591d0a7..08fbb2223 100644
--- a/tests/checks/jobs.fish
+++ b/tests/checks/jobs.fish
@@ -1,22 +1,5 @@
 #RUN: %fish %s
 
-# Ensure there's no zombies before we start, otherwise the tests will mysteriously fail.
-set -l zombies_among_us
-if not contains (uname) SunOS
-    set zombies_among_us (ps -o stat | string match 'Z*' | count)
-else
-    # Solaris' ps is awkward, I don't know if this actually works
-    set zombies_among_us (ps -o s | string match 'Z*' | count)
-end
-
-[ "$zombies_among_us" -eq "0" ]
-or begin
-	echo "Found existing zombie processes. Clean up zombies before running this test."
-	exit 1
-end
-echo "All clear of zombies."
-# CHECK: All clear of zombies.
-
 # Verify zombies are not left by disown (#7183, #5342)
 # Do this first to avoid colliding with the other disowned processes below, which may
 # still be running at the end of the script
@@ -28,13 +11,15 @@ sleep 0.1
 #CHECK: Trigger process reaping
 # The initial approach here was to kill the PID of the sleep process, which should
 # be gone by the time we get here. Unfortunately, kill from procps on pre-2016 distributions
-# does not print an error for non-existent PIDs, so instead look for zombies in this session
-# (there should be none).
+# does not print an error for non-existent PIDs, so instead look for zombies in this session.
+# There could already be zombies from previous tests run in this session or a test could be run
+# simultaneously that causes a zombie to spawn, so limit the output only to processes started by
+# this fish instance.
 if not contains (uname) SunOS
-    ps -o stat | string match 'Z*'
+    ps -o ppid,stat
 else
-    ps -o s | string match 'Z*'
-end
+    ps -o ppid,s
+end | string match -e $fish_pid | string match 'Z*'
 
 # Verify disown can be used with last_pid, even if it is separate from the pgroup.
 # This should silently succeed.