Index: Lib/zipfile.py
===================================================================
--- Lib/zipfile.py	(revision 66890)
+++ Lib/zipfile.py	(working copy)
@@ -1175,8 +1175,9 @@
 
             pos2 = self.fp.tell()
             # Write end-of-zip-archive record
+            dirCount = count
             centDirOffset = pos1
-            if pos1 > ZIP64_LIMIT:
+            if pos1 > ZIP64_LIMIT or count >= ZIP_FILECOUNT_LIMIT:
                 # Need to write the ZIP64 end-of-archive records
                 zip64endrec = struct.pack(
                         structEndArchive64, stringEndArchive64,
@@ -1187,6 +1188,7 @@
                         structEndArchive64Locator,
                         stringEndArchive64Locator, 0, pos2, 1)
                 self.fp.write(zip64locrec)
+                dirCount = 0xFFFF
                 centDirOffset = 0xFFFFFFFF
 
             # check for valid comment length
@@ -1197,8 +1199,7 @@
                 self.comment = self.comment[:ZIP_MAX_COMMENT]
 
             endrec = struct.pack(structEndArchive, stringEndArchive,
-                                 0, 0, count % ZIP_FILECOUNT_LIMIT,
-                                 count % ZIP_FILECOUNT_LIMIT, pos2 - pos1,
+                                 0, 0, dirCount, dirCount, pos2 - pos1,
                                  centDirOffset, len(self.comment))
             self.fp.write(endrec)
             self.fp.write(self.comment)