diff --git a/docs/source/markdown/podman-cp.1.md b/docs/source/markdown/podman-cp.1.md
index 56511c2446..bafbbdf3b5 100644
--- a/docs/source/markdown/podman-cp.1.md
+++ b/docs/source/markdown/podman-cp.1.md
@@ -57,6 +57,8 @@ If you use a : in a local machine path, you must be explicit with a relative or
 
 Using `-` as the *src_path* streams the contents of STDIN as a tar archive. The command extracts the content of the tar to the *DEST_PATH* in the container. In this case, *dest_path* must specify a directory. Using `-` as the *dest_path* streams the contents of the resource (can be a directory) as a tar archive to STDOUT.
 
+Note that `podman cp` ignores permission errors when copying from a running rootless container.  The TTY devices inside a rootless container are owned by the host's root user and hence cannot be read inside the container's user namespace.
+
 ## OPTIONS
 
 ## ALTERNATIVES
diff --git a/libpod/container_copy_linux.go b/libpod/container_copy_linux.go
index 66ccd2f1f4..9dd7e7e9cc 100644
--- a/libpod/container_copy_linux.go
+++ b/libpod/container_copy_linux.go
@@ -14,6 +14,7 @@ import (
 	"github.com/containers/buildah/pkg/chrootuser"
 	"github.com/containers/buildah/util"
 	"github.com/containers/podman/v3/libpod/define"
+	"github.com/containers/podman/v3/pkg/rootless"
 	"github.com/containers/storage"
 	"github.com/containers/storage/pkg/idtools"
 	"github.com/docker/docker/pkg/archive"
@@ -139,6 +140,11 @@ func (c *Container) copyToArchive(ctx context.Context, path string, writer io.Wr
 			ChownDirs:          idPair,
 			ChownFiles:         idPair,
 			Excludes:           []string{"dev", "proc", "sys"},
+			// Ignore EPERMs when copying from rootless containers
+			// since we cannot read TTY devices.  Those are owned
+			// by the host's root and hence "nobody" inside the
+			// container's user namespace.
+			IgnoreUnreadable: rootless.IsRootless() && c.state.State == define.ContainerStateRunning,
 		}
 		return c.joinMountAndExec(ctx,
 			func() error {
diff --git a/test/e2e/cp_test.go b/test/e2e/cp_test.go
index c0fb61544a..c0fb3f8878 100644
--- a/test/e2e/cp_test.go
+++ b/test/e2e/cp_test.go
@@ -212,7 +212,6 @@ var _ = Describe("Podman cp", func() {
 
 	// Copy the root dir "/" of a container to the host.
 	It("podman cp the root directory from the ctr to an existing directory on the host ", func() {
-		SkipIfRootless("cannot copy tty devices in rootless mode")
 		container := "copyroottohost"
 		session := podmanTest.RunTopContainer(container)
 		session.WaitWithDefaultTimeout()