diff --git a/test/e2e/cleanup_test.go b/test/e2e/cleanup_test.go
index 6f2f6a533b..52278a23b6 100644
--- a/test/e2e/cleanup_test.go
+++ b/test/e2e/cleanup_test.go
@@ -1,6 +1,7 @@
 package integration
 
 import (
+	. "github.com/containers/podman/v4/test/utils"
 	. "github.com/onsi/ginkgo/v2"
 	. "github.com/onsi/gomega"
 	. "github.com/onsi/gomega/gexec"
@@ -22,45 +23,45 @@ var _ = Describe("Podman container cleanup", func() {
 	It("podman cleanup container by id", func() {
 		session := podmanTest.Podman([]string{"create", ALPINE, "ls"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		cid := session.OutputToString()
 		session = podmanTest.Podman([]string{"container", "cleanup", cid})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		Expect(session.OutputToString()).To(Equal(cid))
 	})
 
 	It("podman cleanup container by short id", func() {
 		session := podmanTest.Podman([]string{"create", ALPINE, "ls"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		cid := session.OutputToString()
 		shortID := cid[0:10]
 		session = podmanTest.Podman([]string{"container", "cleanup", shortID})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		Expect(session.OutputToString()).To(Equal(shortID))
 	})
 
 	It("podman cleanup container by name", func() {
 		session := podmanTest.Podman([]string{"create", "--name", "foo", ALPINE, "ls"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		session = podmanTest.Podman([]string{"container", "cleanup", "foo"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		Expect(session.OutputToString()).To(Equal("foo"))
 	})
 
 	It("podman cleanup all containers", func() {
 		session := podmanTest.Podman([]string{"create", ALPINE, "ls"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		cid := session.OutputToString()
 
 		session = podmanTest.Podman([]string{"container", "cleanup", "--all"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		Expect(session.OutputToString()).To(Equal(cid))
 	})
 
@@ -68,23 +69,23 @@ var _ = Describe("Podman container cleanup", func() {
 		SkipIfRemote("--latest flag n/a")
 		session := podmanTest.Podman([]string{"create", ALPINE, "ls"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 
 		session = podmanTest.Podman([]string{"create", ALPINE, "ls"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		cid := session.OutputToString()
 
 		session = podmanTest.Podman([]string{"container", "cleanup", "--latest"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		Expect(session.OutputToString()).To(Equal(cid))
 	})
 
 	It("podman cleanup running container", func() {
 		session := podmanTest.RunTopContainer("running")
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		session = podmanTest.Podman([]string{"container", "cleanup", "running"})
 		session.WaitWithDefaultTimeout()
 		Expect(session).Should(Exit(125))
@@ -95,10 +96,10 @@ var _ = Describe("Podman container cleanup", func() {
 		SkipIfRootlessCgroupsV1("Pause is not supported in cgroups v1")
 		session := podmanTest.RunTopContainer("paused")
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		session = podmanTest.Podman([]string{"pause", "paused"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 		session = podmanTest.Podman([]string{"container", "cleanup", "paused"})
 		session.WaitWithDefaultTimeout()
 		Expect(session).Should(Exit(125))
@@ -108,6 +109,6 @@ var _ = Describe("Podman container cleanup", func() {
 		// otherwise it fails with container state improper
 		session = podmanTest.Podman([]string{"unpause", "paused"})
 		session.WaitWithDefaultTimeout()
-		Expect(session).Should(Exit(0))
+		Expect(session).Should(ExitCleanly())
 	})
 })
diff --git a/test/utils/matchers.go b/test/utils/matchers.go
index 5fde262543..731843f04e 100644
--- a/test/utils/matchers.go
+++ b/test/utils/matchers.go
@@ -198,16 +198,25 @@ func (matcher *exitCleanlyMatcher) Match(actual interface{}) (success bool, err
 		return false, nil
 	}
 
-	// FIXME: #19809, "failed to connect to syslog" warnings on f38
-	// FIXME: so, until that is fixed, don't check stderr if containerized
-	if !Containerized() {
-		info := GetHostDistributionInfo()
-		if info.Distribution == "fedora" {
-			if stderr != "" {
-				matcher.msg = fmt.Sprintf("Unexpected warnings seen on stderr: %q", stderr)
-				return false, nil
-			}
-		}
+	// Exit status is 0. Now check for anything on stderr... except:
+
+	if Containerized() {
+		// FIXME: #19809, "failed to connect to syslog" warnings on f38
+		// FIXME: so, until that is fixed, don't check stderr if containerized
+		return true, nil
+	}
+
+	info := GetHostDistributionInfo()
+	if info.Distribution != "fedora" {
+		// runc on debian:
+		// FIXME: #11784 - lstat /sys/fs/.../*.scope: ENOENT
+		// FIXME: #11785 - cannot toggle freezer: cgroups not configured
+		return true, nil
+	}
+
+	if stderr != "" {
+		matcher.msg = fmt.Sprintf("Unexpected warnings seen on stderr: %q", stderr)
+		return false, nil
 	}
 
 	return true, nil