diff --git a/integration/client/client_unix_test.go b/integration/client/client_unix_test.go
index 60b7150b8..38fe9c38a 100644
--- a/integration/client/client_unix_test.go
+++ b/integration/client/client_unix_test.go
@@ -33,9 +33,10 @@ const (
 )
 
 var (
-	testImage    = "ghcr.io/containerd/busybox:1.32"
-	shortCommand = withProcessArgs("true")
-	longCommand  = withProcessArgs("/bin/sh", "-c", "while true; do sleep 1; done")
+	testImage             = "ghcr.io/containerd/busybox:1.32"
+	testMultiLayeredImage = "gcr.io/k8s-cri-containerd/volume-copy-up:2.1"
+	shortCommand          = withProcessArgs("true")
+	longCommand           = withProcessArgs("/bin/sh", "-c", "while true; do sleep 1; done")
 )
 
 func TestImagePullSchema1WithEmptyLayers(t *testing.T) {
diff --git a/integration/client/client_windows_test.go b/integration/client/client_windows_test.go
index 575a06a64..532f177ba 100644
--- a/integration/client/client_windows_test.go
+++ b/integration/client/client_windows_test.go
@@ -30,11 +30,12 @@ const (
 )
 
 var (
-	defaultRoot  = filepath.Join(os.Getenv("programfiles"), "containerd", "root-test")
-	defaultState = filepath.Join(os.Getenv("programfiles"), "containerd", "state-test")
-	testImage    string
-	shortCommand = withTrue()
-	longCommand  = withProcessArgs("ping", "-t", "localhost")
+	defaultRoot           = filepath.Join(os.Getenv("programfiles"), "containerd", "root-test")
+	defaultState          = filepath.Join(os.Getenv("programfiles"), "containerd", "state-test")
+	testImage             string
+	testMultiLayeredImage = "gcr.io/k8s-cri-containerd/volume-copy-up:2.1"
+	shortCommand          = withTrue()
+	longCommand           = withProcessArgs("ping", "-t", "localhost")
 )
 
 func init() {
diff --git a/integration/client/import_test.go b/integration/client/import_test.go
index f8de07eb4..c8a225a0b 100644
--- a/integration/client/import_test.go
+++ b/integration/client/import_test.go
@@ -26,12 +26,17 @@ import (
 	"reflect"
 	"runtime"
 	"testing"
+	"time"
 
 	. "github.com/containerd/containerd"
 	"github.com/containerd/containerd/archive/compression"
 	"github.com/containerd/containerd/archive/tartest"
 	"github.com/containerd/containerd/images"
 	"github.com/containerd/containerd/images/archive"
+	"github.com/containerd/containerd/leases"
+	"github.com/containerd/containerd/oci"
+	"github.com/containerd/containerd/platforms"
+
 	digest "github.com/opencontainers/go-digest"
 	specs "github.com/opencontainers/image-spec/specs-go"
 	ocispec "github.com/opencontainers/image-spec/specs-go/v1"
@@ -40,6 +45,18 @@ import (
 // TestExportAndImport exports testImage as a tar stream,
 // and import the tar stream as a new image.
 func TestExportAndImport(t *testing.T) {
+	testExportImport(t, testImage)
+}
+
+// TestExportAndImportMultiLayer exports testMultiLayeredImage as a tar stream,
+// and import the tar stream as a new image. This should ensure that imported
+// images remain sane, and that the Garbage Collector won't delete part of its
+// content.
+func TestExportAndImportMultiLayer(t *testing.T) {
+	testExportImport(t, testMultiLayeredImage)
+}
+
+func testExportImport(t *testing.T, imageName string) {
 	if testing.Short() {
 		t.Skip()
 	}
@@ -52,17 +69,19 @@ func TestExportAndImport(t *testing.T) {
 	}
 	defer client.Close()
 
-	_, err = client.Fetch(ctx, testImage)
+	_, err = client.Fetch(ctx, imageName)
 	if err != nil {
 		t.Fatal(err)
 	}
 
 	wb := bytes.NewBuffer(nil)
-	err = client.Export(ctx, wb, archive.WithAllPlatforms(), archive.WithImage(client.ImageService(), testImage))
+	err = client.Export(ctx, wb, archive.WithPlatform(platforms.Default()), archive.WithImage(client.ImageService(), imageName))
 	if err != nil {
 		t.Fatal(err)
 	}
 
+	client.ImageService().Delete(ctx, imageName)
+
 	opts := []ImportOpt{
 		WithImageRefTranslator(archive.AddRefPrefix("foo/bar")),
 	}
@@ -71,6 +90,41 @@ func TestExportAndImport(t *testing.T) {
 		t.Fatalf("Import failed: %+v", err)
 	}
 
+	// We need to unpack the image, especially if it's multilayered.
+	for _, img := range imgrecs {
+		image := NewImage(client, img)
+
+		// TODO: Show unpack status
+		t.Logf("unpacking %s (%s)...", img.Name, img.Target.Digest)
+		err = image.Unpack(ctx, "")
+		if err != nil {
+			t.Fatalf("Error while unpacking image: %+v", err)
+		}
+		t.Log("done")
+	}
+
+	// we're triggering the Garbage Collector to do its job.
+	ls := client.LeasesService()
+	l, err := ls.Create(ctx, leases.WithRandomID(), leases.WithExpiration(time.Hour))
+	if err != nil {
+		t.Fatalf("Error while creating lease: %+v", err)
+	}
+	if err = ls.Delete(ctx, l, leases.SynchronousDelete); err != nil {
+		t.Fatalf("Error while deleting lease: %+v", err)
+	}
+
+	image, err := client.GetImage(ctx, imageName)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	id := t.Name()
+	container, err := client.NewContainer(ctx, id, WithNewSnapshot(id, image), WithNewSpec(oci.WithImageConfig(image)))
+	if err != nil {
+		t.Fatalf("Error while creating container: %+v", err)
+	}
+	container.Delete(ctx, WithSnapshotCleanup)
+
 	for _, imgrec := range imgrecs {
 		if imgrec.Name == testImage {
 			continue