diff --git a/cmd/skopeo/completions.go b/cmd/skopeo/completions.go
index 20a2f9d1..fe0f5607 100644
--- a/cmd/skopeo/completions.go
+++ b/cmd/skopeo/completions.go
@@ -1,13 +1,50 @@
 package main
 
 import (
+	"github.com/containers/image/v5/directory"
+	"github.com/containers/image/v5/docker"
+	dockerArchive "github.com/containers/image/v5/docker/archive"
+	ociArchive "github.com/containers/image/v5/oci/archive"
+	oci "github.com/containers/image/v5/oci/layout"
+	"github.com/containers/image/v5/sif"
 	"github.com/containers/image/v5/tarball"
 	"github.com/containers/image/v5/transports"
 	"github.com/spf13/cobra"
+	"strings"
 )
 
-// autocompleteSupportedTransports list all supported transports with the colon suffix.
-func autocompleteSupportedTransports(cmd *cobra.Command, args []string, toComplete string) ([]cobra.Completion, cobra.ShellCompDirective) {
+func autocompleteImageNames(cmd *cobra.Command, args []string, toComplete string) ([]cobra.Completion, cobra.ShellCompDirective) {
+	transport, details, haveTransport := strings.Cut(toComplete, ":")
+	if !haveTransport {
+		transports := supportedTransportSuggestions()
+		return transports, cobra.ShellCompDirectiveNoSpace | cobra.ShellCompDirectiveNoFileComp
+	}
+	switch transport {
+	case ociArchive.Transport.Name(), dockerArchive.Transport.Name():
+		// Can have [:{*reference|@source-index}]
+		// FIXME: `oci-archive:/path/to/a.oci:<TAB>` completes paths
+		return nil, cobra.ShellCompDirectiveNoSpace
+	case sif.Transport.Name():
+		return nil, cobra.ShellCompDirectiveDefault
+
+	// Both directory and oci should have ShellCompDirectiveFilterDirs to complete only directories, but it doesn't currently work in bash: https://github.com/spf13/cobra/issues/2242
+	case oci.Transport.Name():
+		// Can have '[:{reference|@source-index}]'
+		// FIXME: `oci:/path/to/dir/:<TAB>` completes paths
+		return nil, cobra.ShellCompDirectiveDefault | cobra.ShellCompDirectiveNoSpace
+	case directory.Transport.Name():
+		return nil, cobra.ShellCompDirectiveDefault
+
+	case docker.Transport.Name():
+		if details == "" {
+			return []cobra.Completion{transport + "://"}, cobra.ShellCompDirectiveNoSpace | cobra.ShellCompDirectiveNoFileComp
+		}
+	}
+	return nil, cobra.ShellCompDirectiveNoSpace | cobra.ShellCompDirectiveNoFileComp
+}
+
+// supportedTransportSuggestions list all supported transports with the colon suffix.
+func supportedTransportSuggestions() []string {
 	tps := transports.ListNames()
 	suggestions := make([]cobra.Completion, 0, len(tps))
 	for _, tp := range tps {
@@ -18,5 +55,5 @@ func autocompleteSupportedTransports(cmd *cobra.Command, args []string, toComple
 			suggestions = append(suggestions, tp+":")
 		}
 	}
-	return suggestions, cobra.ShellCompDirectiveNoFileComp | cobra.ShellCompDirectiveNoSpace
+	return suggestions
 }
diff --git a/cmd/skopeo/copy.go b/cmd/skopeo/copy.go
index db13c998..9d47a5c4 100644
--- a/cmd/skopeo/copy.go
+++ b/cmd/skopeo/copy.go
@@ -71,7 +71,7 @@ See skopeo(1) section "IMAGE NAMES" for the expected format
 `, strings.Join(transports.ListNames(), ", ")),
 		RunE:              commandAction(opts.run),
 		Example:           `skopeo copy docker://quay.io/skopeo/stable:latest docker://registry.example.com/skopeo:latest`,
-		ValidArgsFunction: autocompleteSupportedTransports,
+		ValidArgsFunction: autocompleteImageNames,
 	}
 	adjustUsage(cmd)
 	flags := cmd.Flags()
diff --git a/cmd/skopeo/delete.go b/cmd/skopeo/delete.go
index 84ed5f97..ddfc2cbe 100644
--- a/cmd/skopeo/delete.go
+++ b/cmd/skopeo/delete.go
@@ -37,7 +37,7 @@ See skopeo(1) section "IMAGE NAMES" for the expected format
 `, strings.Join(transports.ListNames(), ", ")),
 		RunE:              commandAction(opts.run),
 		Example:           `skopeo delete docker://registry.example.com/example/pause:latest`,
-		ValidArgsFunction: autocompleteSupportedTransports,
+		ValidArgsFunction: autocompleteImageNames,
 	}
 	adjustUsage(cmd)
 	flags := cmd.Flags()
diff --git a/cmd/skopeo/inspect.go b/cmd/skopeo/inspect.go
index 4ca03ac1..843f26e9 100644
--- a/cmd/skopeo/inspect.go
+++ b/cmd/skopeo/inspect.go
@@ -53,7 +53,7 @@ See skopeo(1) section "IMAGE NAMES" for the expected format
 		Example: `skopeo inspect docker://registry.fedoraproject.org/fedora
 skopeo inspect --config docker://docker.io/alpine
 skopeo inspect --format "Name: {{.Name}} Digest: {{.Digest}}" docker://registry.access.redhat.com/ubi8`,
-		ValidArgsFunction: autocompleteSupportedTransports,
+		ValidArgsFunction: autocompleteImageNames,
 	}
 	adjustUsage(cmd)
 	flags := cmd.Flags()