diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 596b0ad..1f08258 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -141,11 +141,25 @@
 
 class MiscReadTest(ReadTest):
 
-    def test_no_filename(self):
+    def test_no_name_argument(self):
         fobj = open(self.tarname, "rb")
         tar = tarfile.open(fileobj=fobj, mode=self.mode)
         self.assertEqual(tar.name, os.path.abspath(fobj.name))
 
+    def test_no_name_attribute(self):
+        data = open(self.tarname, "rb").read()
+        fobj = StringIO.StringIO(data)
+        self.assertRaises(AttributeError, getattr, fobj, "name")
+        tar = tarfile.open(fileobj=fobj, mode=self.mode)
+        self.assertEqual(tar.name, None)
+
+    def test_empty_name_attribute(self):
+        data = open(self.tarname, "rb").read()
+        fobj = StringIO.StringIO(data)
+        fobj.name = ""
+        tar = tarfile.open(fileobj=fobj, mode=self.mode)
+        self.assertEqual(tar.name, None)
+
     def test_fail_comp(self):
         # For Gzip and Bz2 Tests: fail with a ReadError on an uncompressed file.
         if self.mode == "r:":