diff --git a/cmd/ctr/commands/images/import.go b/cmd/ctr/commands/images/import.go
index e7a494579..ab1fbb2cd 100644
--- a/cmd/ctr/commands/images/import.go
+++ b/cmd/ctr/commands/images/import.go
@@ -60,6 +60,10 @@ If foobar.tar contains an OCI ref named "latest" and anonymous ref "sha256:deadb
 			Name:  "digests",
 			Usage: "whether to create digest images (default: false)",
 		},
+		cli.BoolFlag{
+			Name:  "skip-digest-for-named",
+			Usage: "skip applying --digests option to images named in the importing tar (use it in conjunction with --digests)",
+		},
 		cli.StringFlag{
 			Name:  "index-name",
 			Usage: "image name to keep index as, by default index is discarded",
@@ -96,6 +100,12 @@ If foobar.tar contains an OCI ref named "latest" and anonymous ref "sha256:deadb
 		if context.Bool("digests") {
 			opts = append(opts, containerd.WithDigestRef(archive.DigestTranslator(prefix)))
 		}
+		if context.Bool("skip-digest-for-named") {
+			if !context.Bool("digests") {
+				return fmt.Errorf("--skip-digest-for-named must be specified with --digests option")
+			}
+			opts = append(opts, containerd.WithSkipDigestRef(func(name string) bool { return name != "" }))
+		}
 
 		if idxName := context.String("index-name"); idxName != "" {
 			opts = append(opts, containerd.WithIndexName(idxName))
diff --git a/import.go b/import.go
index 6080161f8..2ba717448 100644
--- a/import.go
+++ b/import.go
@@ -34,6 +34,7 @@ type importOpts struct {
 	indexName    string
 	imageRefT    func(string) string
 	dgstRefT     func(digest.Digest) string
+	skipDgstRef  func(string) bool
 	allPlatforms bool
 	compress     bool
 }
@@ -59,6 +60,17 @@ func WithDigestRef(f func(digest.Digest) string) ImportOpt {
 	}
 }
 
+// WithSkipDigestRef is used to specify when to skip applying
+// WithDigestRef. The callback receives an image reference (or an empty
+// string if not specified in the image). When the callback returns true,
+// the skip occurs.
+func WithSkipDigestRef(f func(string) bool) ImportOpt {
+	return func(c *importOpts) error {
+		c.skipDgstRef = f
+		return nil
+	}
+}
+
 // WithIndexName creates a tag pointing to the imported index
 func WithIndexName(name string) ImportOpt {
 	return func(c *importOpts) error {
@@ -152,6 +164,11 @@ func (c *Client) Import(ctx context.Context, reader io.Reader, opts ...ImportOpt
 					Target: m,
 				})
 			}
+			if iopts.skipDgstRef != nil {
+				if iopts.skipDgstRef(name) {
+					continue
+				}
+			}
 			if iopts.dgstRefT != nil {
 				ref := iopts.dgstRefT(m.Digest)
 				if ref != "" {