diff --git a/mem/file.go b/mem/file.go
index 9096ff0..3c1e09a 100644
--- a/mem/file.go
+++ b/mem/file.go
@@ -59,7 +59,9 @@ type FileData struct {
 	modtime time.Time
 }
 
-func (d FileData) Name() string {
+func (d *FileData) Name() string {
+	d.Lock()
+	defer d.Unlock()
 	return d.name
 }
 
@@ -107,9 +109,7 @@ func (f *File) Close() error {
 }
 
 func (f *File) Name() string {
-	f.fileData.Lock()
-	defer f.fileData.Unlock()
-	return f.fileData.name
+	return f.fileData.Name()
 }
 
 func (f *File) Stat() (os.FileInfo, error) {
diff --git a/memmap_test.go b/memmap_test.go
index 44d525b..9efd1f2 100644
--- a/memmap_test.go
+++ b/memmap_test.go
@@ -259,3 +259,26 @@ func TestWriteCloseTime(t *testing.T) {
 		}
 	}
 }
+
+// This test should be run with the race detector on:
+// go test -race -v -timeout 10s -run TestRacingDeleteAndClose
+func TestRacingDeleteAndClose(t *testing.T) {
+	fs := NewMemMapFs()
+	pathname := "testfile"
+	f, err := fs.Create(pathname)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	in := make(chan bool)
+
+	go func() {
+		<-in
+		f.Close()
+	}()
+	go func() {
+		<-in
+		fs.Remove(pathname)
+	}()
+	close(in)
+}