diff --git a/libpod/healthcheck.go b/libpod/healthcheck.go
index 96740d2c13..ada4e004d3 100644
--- a/libpod/healthcheck.go
+++ b/libpod/healthcheck.go
@@ -15,6 +15,7 @@ import (
 	"time"
 
 	"github.com/containers/podman/v5/libpod/define"
+	"github.com/containers/podman/v5/libpod/shutdown"
 	"github.com/sirupsen/logrus"
 	"golang.org/x/sys/unix"
 )
@@ -273,6 +274,13 @@ func (c *Container) incrementStartupHCSuccessCounter(ctx context.Context) {
 		// Which happens to be us.
 		// So this has to be last - after this, systemd serves us a
 		// SIGTERM and we exit.
+		// Special case, via SIGTERM we exit(1) which means systemd logs a failure in the unit.
+		// We do not want this as the unit will be leaked on failure states unless "reset-failed"
+		// is called. Fundamentally this is expected so switch it to exit 0.
+		// NOTE: This is only safe while being called from "podman healthcheck run" which we know
+		// is the case here as we should not alter the exit code of another process that just
+		// happened to call this.
+		shutdown.SetExitCode(0)
 		if err := c.removeTransientFiles(ctx, true, oldUnit); err != nil {
 			logrus.Errorf("Error removing container %s healthcheck: %v", c.ID(), err)
 			return
diff --git a/test/system/220-healthcheck.bats b/test/system/220-healthcheck.bats
index 662ecf8ff6..f232d6ea4f 100644
--- a/test/system/220-healthcheck.bats
+++ b/test/system/220-healthcheck.bats
@@ -98,7 +98,11 @@ Log[-1].Output   | \"Uh-oh on stdout!\\\nUh-oh on stderr!\\\n\"
 
     # Check that we now we do have valid podman units with this
     # name so that the leak check below does not turn into a NOP without noticing.
-    assert "$(systemctl list-units --type timer | grep $cid)" =~ "podman" "Healthcheck systemd unit exists"
+    run -0 systemctl list-units
+    cidmatch=$(grep "$cid" <<<"$output")
+    echo "$cidmatch"
+    assert "$cidmatch" =~ " $cid-[0-9a-f]+\.timer  *.*/podman healthcheck run $cid" \
+           "Healthcheck systemd unit exists"
 
     current_time=$(date --iso-8601=ns)
     # After three successive failures, container should no longer be healthy
@@ -117,7 +121,12 @@ Log[-1].Output   | \"Uh-oh on stdout!\\\nUh-oh on stderr!\\\n\"
 
     # Important check for https://github.com/containers/podman/issues/22884
     # We never should leak the unit files, healthcheck uses the cid in name so just grep that.
-    assert "$(systemctl list-units --type timer | grep $cid)" == "" "Healthcheck systemd unit cleanup"
+    # (Ignore .scope units, those are conmon and can linger for 5 minutes)
+    # (Ignore .mount, too. They are created/removed by systemd based on the actual real mounts
+    #  on the host and that is async and might be slow enough in CI to cause failures.)
+    run -0 systemctl list-units --quiet "*$cid*"
+    except_scope_mount=$(grep -vF ".scope " <<<"$output" | { grep -vF ".mount" || true; } )
+    assert "$except_scope_mount" == "" "Healthcheck systemd unit cleanup: no units leaked"
 }
 
 @test "podman healthcheck - restart cleans up old state" {