diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index f653399d2..a38c01519 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -322,6 +322,22 @@ jobs:
           sudo GOPATH=$GOPATH GOPROXY=$GOPROXY TEST_RUNTIME=$TEST_RUNTIME RUNC_FLAVOR=$RUNC_FLAVOR TESTFLAGS_PARALLEL=1 make integration EXTRA_TESTFLAGS=-no-criu
         working-directory: src/github.com/containerd/containerd
 
+      # CRIU wouldn't work with overlay snapshotter yet.
+      # See https://github.com/containerd/containerd/pull/4708#issuecomment-724322294.
+      - name: CRIU Integration
+        env:
+          GOPROXY: direct
+          TEST_RUNTIME: ${{ matrix.runtime }}
+          RUNC_FLAVOR: ${{ matrix.runc }}
+        # crun doesn't have "checkpoint" command.
+        if: ${{ matrix.runc == 'runc' }}
+        run: |
+          sudo GOPATH=$GOPATH GOPROXY=$GOPROXY \
+          TEST_RUNTIME=$TEST_RUNTIME RUNC_FLAVOR=$RUNC_FLAVOR TESTFLAGS_PARALLEL=1 \
+          TEST_SNAPSHOTTER=native \
+          make integration EXTRA_TESTFLAGS='-run TestCheckpoint'
+        working-directory: src/github.com/containerd/containerd
+
       - name: CRI Integration Test
         env:
           TEST_RUNTIME: ${{ matrix.runtime }}
diff --git a/integration/client/client_test.go b/integration/client/client_test.go
index 2ad73c001..ddb6889a5 100644
--- a/integration/client/client_test.go
+++ b/integration/client/client_test.go
@@ -50,6 +50,7 @@ var (
 	noCriu            bool
 	supportsCriu      bool
 	testNamespace     = "testing"
+	testSnapshotter   = DefaultSnapshotter
 	ctrdStdioFilePath string
 
 	ctrd = &daemon{}
@@ -132,11 +133,30 @@ func TestMain(m *testing.M) {
 
 	// allow comparison with containerd under test
 	log.G(ctx).WithFields(logrus.Fields{
-		"version":  version.Version,
-		"revision": version.Revision,
-		"runtime":  os.Getenv("TEST_RUNTIME"),
+		"version":     version.Version,
+		"revision":    version.Revision,
+		"runtime":     os.Getenv("TEST_RUNTIME"),
+		"snapshotter": os.Getenv("TEST_SNAPSHOTTER"),
 	}).Info("running tests against containerd")
 
+	snapshotter := DefaultSnapshotter
+	if ss := os.Getenv("TEST_SNAPSHOTTER"); ss != "" {
+		snapshotter = ss
+	}
+
+	ns, ok := namespaces.Namespace(ctx)
+	if !ok {
+		fmt.Fprintln(os.Stderr, "error getting namespace")
+		os.Exit(1)
+	}
+	err = client.NamespaceService().SetLabel(ctx, ns, defaults.DefaultSnapshotterNSLabel, snapshotter)
+	if err != nil {
+		fmt.Fprintf(os.Stderr, "error setting %s's default snapshotter as %s: %s\n", ns, snapshotter, err)
+		os.Exit(1)
+	}
+
+	testSnapshotter = snapshotter
+
 	// pull a seed image
 	log.G(ctx).WithField("image", testImage).Info("start to pull seed image")
 	if _, err = client.Pull(ctx, testImage, WithPullUnpack); err != nil {
@@ -285,7 +305,7 @@ func TestImagePullWithDiscardContent(t *testing.T) {
 		t.Fatalf("there is no layers in the target image(parent: %v)", img.Target())
 	}
 	var (
-		sn    = client.SnapshotService("")
+		sn    = client.SnapshotService(testSnapshotter)
 		chain []digest.Digest
 	)
 	for i, dgst := range layers {
diff --git a/integration/client/container_checkpoint_test.go b/integration/client/container_checkpoint_test.go
index 193ceaee7..930b6991b 100644
--- a/integration/client/container_checkpoint_test.go
+++ b/integration/client/container_checkpoint_test.go
@@ -414,7 +414,7 @@ func TestCheckpointLeaveRunning(t *testing.T) {
 	<-statusC
 }
 
-func TestCRWithImagePath(t *testing.T) {
+func TestCheckpointRestoreWithImagePath(t *testing.T) {
 	if !supportsCriu {
 		t.Skip("system does not have criu installed")
 	}