diff --git a/test/e2e/common_test.go b/test/e2e/common_test.go
index 2e48e1763f..d03a2741b1 100644
--- a/test/e2e/common_test.go
+++ b/test/e2e/common_test.go
@@ -645,9 +645,13 @@ func isRootless() bool {
 	return os.Geteuid() != 0
 }
 
+func isCgroupsV1() bool {
+	return !CGROUPSV2
+}
+
 func SkipIfCgroupV1(reason string) {
 	checkReason(reason)
-	if !CGROUPSV2 {
+	if isCgroupsV1() {
 		Skip(reason)
 	}
 }
diff --git a/test/e2e/stats_test.go b/test/e2e/stats_test.go
index a0be5d4627..c0d56fdbca 100644
--- a/test/e2e/stats_test.go
+++ b/test/e2e/stats_test.go
@@ -22,6 +22,9 @@ var _ = Describe("Podman stats", func() {
 
 	BeforeEach(func() {
 		SkipIfRootlessCgroupsV1("stats not supported on cgroupv1 for rootless users")
+		if isContainerized() {
+			SkipIfCgroupV1("stats not supported inside cgroupv1 container environment")
+		}
 		var err error
 		tempdir, err = CreateTempDirInTempDir()
 		if err != nil {
diff --git a/test/e2e/systemd_test.go b/test/e2e/systemd_test.go
index bb51d6ac2f..3213a839a6 100644
--- a/test/e2e/systemd_test.go
+++ b/test/e2e/systemd_test.go
@@ -6,7 +6,6 @@ import (
 	"strings"
 	"time"
 
-	"github.com/containers/podman/v3/pkg/rootless"
 	. "github.com/containers/podman/v3/test/utils"
 	. "github.com/onsi/ginkgo"
 	. "github.com/onsi/gomega"
@@ -118,11 +117,13 @@ WantedBy=multi-user.target
 		Expect(len(conData)).To(Equal(1))
 		Expect(conData[0].Config.SystemdMode).To(BeTrue())
 
-		if CGROUPSV2 || !rootless.IsRootless() {
-			stats := podmanTest.Podman([]string{"stats", "--no-stream", ctrName})
-			stats.WaitWithDefaultTimeout()
-			Expect(stats).Should(Exit(0))
+		// stats not supported w/ CGv1 rootless or containerized
+		if isCgroupsV1() && (isRootless() || isContainerized()) {
+			return
 		}
+		stats := podmanTest.Podman([]string{"stats", "--no-stream", ctrName})
+		stats.WaitWithDefaultTimeout()
+		Expect(stats).Should(Exit(0))
 	})
 
 	It("podman create container with systemd entrypoint triggers systemd mode", func() {