diff -r a707f3cc0e8e Lib/tarfile.py
--- a/Lib/tarfile.py	Mon Jan 13 14:24:11 2014 +0200
+++ b/Lib/tarfile.py	Mon Jan 13 16:31:33 2014 +0200
@@ -1617,7 +1617,7 @@
             if not extfileobj and fileobj is not None:
                 fileobj.close()
             raise
-        t._extfileobj = extfileobj
+        t._extfileobj = False
         return t
 
     @classmethod
diff -r a707f3cc0e8e Lib/test/test_tarfile.py
--- a/Lib/test/test_tarfile.py	Mon Jan 13 14:24:11 2014 +0200
+++ b/Lib/test/test_tarfile.py	Mon Jan 13 16:31:33 2014 +0200
@@ -841,6 +841,12 @@
         tar.addfile(tarfile.TarInfo("foo"))
         tar.close()
         self.assertFalse(fobj.closed, "external fileobjs must never closed")
+        # Issue #20238: Incomplete gzip output with mode="w:gz"
+        data = fobj.getvalue()
+        del tar
+        support.gc_collect()
+        self.assertFalse(fobj.closed)
+        self.assertEqual(data, fobj.getvalue())
 
 
 class WriteTest(WriteTestBase, unittest.TestCase):