diff --git a/test/e2e/cleanup_test.go b/test/e2e/cleanup_test.go
index 46e88804a8..1563212c0d 100644
--- a/test/e2e/cleanup_test.go
+++ b/test/e2e/cleanup_test.go
@@ -124,5 +124,11 @@ var _ = Describe("Podman container cleanup", func() {
 		session.WaitWithDefaultTimeout()
 		Expect(session).Should(Exit(125))
 		Expect(session.ErrorToString()).To(ContainSubstring("container state improper"))
+
+		// unpause so that the cleanup can stop the container,
+		// otherwise it fails with container state improper
+		session = podmanTest.Podman([]string{"unpause", "paused"})
+		session.WaitWithDefaultTimeout()
+		Expect(session).Should(Exit(0))
 	})
 })
diff --git a/test/e2e/pause_test.go b/test/e2e/pause_test.go
index b67a46e1c1..d91fc018ac 100644
--- a/test/e2e/pause_test.go
+++ b/test/e2e/pause_test.go
@@ -151,6 +151,11 @@ var _ = Describe("Podman pause", func() {
 		Expect(podmanTest.NumberOfContainersRunning()).To(Equal(0))
 		Expect(strings.ToLower(podmanTest.GetContainerStatus())).To(ContainSubstring(pausedState))
 
+		// unpause so that the cleanup can stop the container,
+		// otherwise it fails with container state improper
+		session = podmanTest.Podman([]string{"unpause", cid})
+		session.WaitWithDefaultTimeout()
+		Expect(session).Should(Exit(0))
 	})
 
 	It("podman remove a paused container by id with force", func() {