diff --git a/Lib/test/test_zipfile.py b/Lib/test/test_zipfile.py
index 1fed79a..a2c3a2c 100644
--- a/Lib/test/test_zipfile.py
+++ b/Lib/test/test_zipfile.py
@@ -664,6 +664,16 @@
         # quickly.
         self.assertRaises(IOError, zipfile.ZipFile, TESTFN)
 
+    def test_empty_file_raises_BadZipFile(self):
+        f = open(TESTFN, 'w')
+        f.close()
+        self.assertRaises(zipfile.BadZipfile, zipfile.ZipFile, TESTFN)
+
+        f = open(TESTFN, 'w')
+        f.write("short file")
+        f.close()
+        self.assertRaises(zipfile.BadZipfile, zipfile.ZipFile, TESTFN)
+
     def testClosedZipRaisesRuntimeError(self):
         # Verify that testzip() doesn't swallow inappropriate exceptions.
         data = StringIO()