diff --git a/internal/cli/compose_up.go b/internal/cli/compose_up.go
index e1bcc04..4573cc5 100644
--- a/internal/cli/compose_up.go
+++ b/internal/cli/compose_up.go
@@ -469,9 +469,9 @@ func (r *upRunner) buildAndExtendCompose(ctx context.Context, s composeStart, pe
 		if opts.omitSyntaxDirective {
 			syntax = ""
 		}
-		dstFolder = filepath.Join(cacheFolder(), "container-features", fmt.Sprintf("%s-%d", cliVersion(), time.Now().UnixMilli()))
-		if err := os.MkdirAll(dstFolder, 0o755); err != nil {
-			return nil, fmt.Errorf("create features folder: %w", err)
+		var err error
+		if dstFolder, err = createFeaturesFolder(); err != nil {
+			return nil, err
 		}
 		info = imagemeta.GenerateComposeLabelBuild(baseName, labelMetadata, syntax)
 	default:
diff --git a/internal/cli/feature_install.go b/internal/cli/feature_install.go
index 8b09244..d0b814f 100644
--- a/internal/cli/feature_install.go
+++ b/internal/cli/feature_install.go
@@ -127,12 +127,25 @@ func (r localFeatureRoots) resolve(logger log.Logger, id string) (string, bool,
 
 // createFeaturesFolder creates the folder the Features are staged in, TS
 // createFeaturesTempFolder: <cacheFolder>/container-features/<cliVersion>-<ms>.
+// The folder is this run's alone: runs started in the same millisecond would
+// otherwise share it, and one run's realignFeatureDirs renames and removes the
+// other's .stage- folders. A name another run holds moves to the next
+// millisecond.
 func createFeaturesFolder() (string, error) {
-	dir := filepath.Join(cacheFolder(), "container-features", fmt.Sprintf("%s-%d", cliVersion(), time.Now().UnixMilli()))
-	if err := os.MkdirAll(dir, 0o755); err != nil {
+	parent := filepath.Join(cacheFolder(), "container-features")
+	if err := os.MkdirAll(parent, 0o755); err != nil {
 		return "", fmt.Errorf("create features folder: %w", err)
 	}
-	return dir, nil
+	for ms := time.Now().UnixMilli(); ; ms++ {
+		dir := filepath.Join(parent, fmt.Sprintf("%s-%d", cliVersion(), ms))
+		err := os.Mkdir(dir, 0o755)
+		if err == nil {
+			return dir, nil
+		}
+		if !errors.Is(err, os.ErrExist) {
+			return "", fmt.Errorf("create features folder: %w", err)
+		}
+	}
 }
 
 // fetchFeatureSetsWithOrder resolves the feature dependency graph through the
diff --git a/internal/cli/feature_install_test.go b/internal/cli/feature_install_test.go
index 8f19669..08716e4 100644
--- a/internal/cli/feature_install_test.go
+++ b/internal/cli/feature_install_test.go
@@ -460,3 +460,22 @@ func TestReadConfigurationRefusesALocalFeatureOutsideDevcontainer(t *testing.T)
 	}
 	wantExitCode(t, err, 1)
 }
+
+// Runs started in the same millisecond each get a features folder of their
+// own: a shared one let one run's realignFeatureDirs remove the other's
+// .stage- folders ("stage feature h_0: lstat .../.stage-0: no such file or
+// directory" in the parity lane).
+func TestCreateFeaturesFolderIsTheRunsAlone(t *testing.T) {
+	t.Setenv("TMPDIR", t.TempDir())
+	seen := map[string]bool{}
+	for range 50 {
+		dir, err := createFeaturesFolder()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if seen[dir] {
+			t.Fatalf("%s handed out twice", dir)
+		}
+		seen[dir] = true
+	}
+}