Index: Lib/zipfile.py
===================================================================
--- Lib/zipfile.py	(revision 84573)
+++ Lib/zipfile.py	(working copy)
@@ -1056,13 +1056,13 @@
             # Must overwrite CRC and sizes with correct data later
             zinfo.CRC = CRC = 0
             zinfo.compress_size = compress_size = 0
-            zinfo.file_size = file_size = 0
             self.fp.write(zinfo.FileHeader())
             if zinfo.compress_type == ZIP_DEFLATED:
                 cmpr = zlib.compressobj(zlib.Z_DEFAULT_COMPRESSION,
                      zlib.DEFLATED, -15)
             else:
                 cmpr = None
+            file_size = 0
             while 1:
                 buf = fp.read(1024 * 8)
                 if not buf:
@@ -1082,11 +1082,11 @@
             zinfo.compress_size = file_size
         zinfo.CRC = CRC
         zinfo.file_size = file_size
-        # Seek backwards and write CRC and file sizes
+        # Seek backwards and write file header (which will now include
+        # correct CRC and file sizes)
         position = self.fp.tell()       # Preserve current position in file
-        self.fp.seek(zinfo.header_offset + 14, 0)
-        self.fp.write(struct.pack("<LLL", zinfo.CRC, zinfo.compress_size,
-              zinfo.file_size))
+        self.fp.seek(zinfo.header_offset, 0)
+        self.fp.write(zinfo.FileHeader())
         self.fp.seek(position, 0)
         self.filelist.append(zinfo)
         self.NameToInfo[zinfo.filename] = zinfo
Index: Lib/test/test_zipfile64.py
===================================================================
--- Lib/test/test_zipfile64.py	(revision 84573)
+++ Lib/test/test_zipfile64.py	(working copy)
@@ -31,17 +31,12 @@
 # How much time in seconds can pass before we print a 'Still working' message.
 _PRINT_WORKING_MSG_INTERVAL = 5 * 60
 
-class TestsWithSourceFile(unittest.TestCase):
+class TestsWithSmallSourceFile(unittest.TestCase):
     def setUp(self):
         # Create test data.
         line_gen = ("Test of zipfile line %d." % i for i in range(1000000))
         self.data = '\n'.join(line_gen).encode('ascii')
 
-        # And write it to a file.
-        fp = open(TESTFN, "wb")
-        fp.write(self.data)
-        fp.close()
-
     def zipTest(self, f, compression):
         # Create the ZIP archive.
         zipfp = zipfile.ZipFile(f, "w", compression, allowZip64=True)
@@ -63,7 +58,7 @@
         zipfp.close()
 
         # Read the ZIP archive
-        zipfp = zipfile.ZipFile(f, "r", compression)
+        zipfp = zipfile.ZipFile(f, "r")
         for num in range(filecount):
             self.assertEqual(zipfp.read("testfn%d" % num), self.data)
             # Print still working message since this test can be really slow
@@ -89,11 +84,52 @@
                 self.zipTest(f, zipfile.ZIP_DEFLATED)
 
     def tearDown(self):
+        if os.path.exists(TESTFN2):
+            os.remove(TESTFN2)
+
+
+class TestsWithHugeSourceFile(unittest.TestCase):
+    def setUp(self):
+        # Create test data.
+        line_gen = ("Test of zipfile line %d." % i for i in range(1000000))
+        self.data = '\n'.join(line_gen).encode('ascii')
+        
+        # Write enough copies of it into a file to make >4GB
+        self.num_copies = 1 + (4*1024**3) // len(self.data)
+        f = open(TESTFN, "wb")
+        for i in range(self.num_copies):
+            f.write(self.data)
+        f.close()
+
+    def zipTest(self, f, compression):
+        # Create the ZIP archive.
+        zipfp = zipfile.ZipFile(f, "w", compression, allowZip64=True)
+        zipfp.write(TESTFN, arcname="testfile")
+        zipfp.close()
+
+        # Read the ZIP archive and verify its contents
+        zipfp = zipfile.ZipFile(f, "r")
+        f = zipfp.open("testfile")
+        for i in range(self.num_copies):
+            d = f.read(len(self.data))
+            self.assertEqual(d, self.data)
+        # check that further reads retrieve no data
+        self.assertEqual(f.read(1), b"")
+        zipfp.close()
+
+    def testStored(self):
+        self.zipTest(TESTFN2, zipfile.ZIP_STORED)
+
+    if zlib:
+        def testDeflated(self):
+            self.zipTest(TESTFN2, zipfile.ZIP_DEFLATED)
+
+    def tearDown(self):
         for fname in TESTFN, TESTFN2:
             if os.path.exists(fname):
                 os.remove(fname)
+                
 
-
 class OtherTests(unittest.TestCase):
     def testMoreThan64kFiles(self):
         # This test checks that more than 64k files can be added to an archive,
@@ -112,13 +148,12 @@
             content = zipf2.read("foo%08d" % i).decode('ascii')
             self.assertEqual(content, "%d" % (i**3 % 57))
         zipf.close()
-
+        
     def tearDown(self):
         support.unlink(TESTFN)
-        support.unlink(TESTFN2)
 
 def test_main():
-    run_unittest(TestsWithSourceFile, OtherTests)
+    run_unittest(TestsWithSmallSourceFile, TestsWithHugeSourceFile, OtherTests)
 
 if __name__ == "__main__":
     test_main()