diff --git a/basepath.go b/basepath.go
index 616ff8f..584320a 100644
--- a/basepath.go
+++ b/basepath.go
@@ -30,7 +30,9 @@ type BasePathFile struct {
 
 func (f *BasePathFile) Name() string {
 	sourcename := f.File.Name()
-	return strings.TrimPrefix(sourcename, filepath.Clean(f.path))
+	sourcename = strings.TrimPrefix(sourcename, filepath.VolumeName(sourcename))
+	sourcename = strings.TrimPrefix(sourcename, filepath.Clean(f.path))
+	return sourcename
 }
 
 func NewBasePathFs(source Fs, path string) Fs {
diff --git a/composite_test.go b/composite_test.go
index 3682c3c..96f45ef 100644
--- a/composite_test.go
+++ b/composite_test.go
@@ -479,7 +479,7 @@ func TestUnionFileReaddirAskForTooMany(t *testing.T) {
 	overlay := &MemMapFs{}
 
 	for i := 0; i < 5; i++ {
-		WriteFile(base, fmt.Sprintf("file%d.txt", i), []byte("afero"), 0777)
+		WriteFile(base, fmt.Sprintf("/file%d.txt", i), []byte("afero"), 0777)
 	}
 
 	ufs := &CopyOnWriteFs{base: base, layer: overlay}
diff --git a/memmap.go b/memmap.go
index b2dca4f..164ca5a 100644
--- a/memmap.go
+++ b/memmap.go
@@ -191,7 +191,7 @@ func normalizePath(path string) (string, error) {
 	case FilePathSeparator:
 		return rootAbs, nil
 	default:
-		return path, nil
+		return filepath.Abs(path)
 	}
 }