diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index 3ab66ce..1d10650 100644
--- a/Lib/zipfile.py
+++ b/Lib/zipfile.py
@@ -772,6 +772,7 @@
                 # set the modified flag so central directory gets written
                 # even if no files are added to the archive
                 self._didModify = True
+                self._start_disk = self.fp.tell()
             elif key == 'a':
                 try:
                     # See if file is a zip file
@@ -785,6 +786,7 @@
                     # set the modified flag so central directory gets written
                     # even if no files are added to the archive
                     self._didModify = True
+                    self._start_disk = self.fp.tell()
             else:
                 raise RuntimeError('Mode must be "r", "w" or "a"')
         except:
@@ -815,17 +817,18 @@
         offset_cd = endrec[_ECD_OFFSET]         # offset of central directory
         self._comment = endrec[_ECD_COMMENT]    # archive comment
 
-        # "concat" is zero, unless zip was concatenated to another file
-        concat = endrec[_ECD_LOCATION] - size_cd - offset_cd
+        # self._start_disk:  Position of the start of ZIP archive
+        # It is zero, unless ZIP was concatenated to another file
+        self._start_disk = endrec[_ECD_LOCATION] - size_cd - offset_cd
         if endrec[_ECD_SIGNATURE] == stringEndArchive64:
             # If Zip64 extension structures are present, account for them
-            concat -= (sizeEndCentDir64 + sizeEndCentDir64Locator)
+            self._start_disk -= (sizeEndCentDir64 + sizeEndCentDir64Locator)
 
         if self.debug > 2:
-            inferred = concat + offset_cd
-            print "given, inferred, offset", offset_cd, inferred, concat
+            inferred = self._start_disk + offset_cd
+            print "given, inferred, offset", offset_cd, inferred, self._start_disk
         # self.start_dir:  Position of start of central directory
-        self.start_dir = offset_cd + concat
+        self.start_dir = offset_cd + self._start_disk
         fp.seek(self.start_dir, 0)
         data = fp.read(size_cd)
         fp = cStringIO.StringIO(data)
@@ -855,7 +858,7 @@
                                      t>>11, (t>>5)&0x3F, (t&0x1F) * 2 )
 
             x._decodeExtra()
-            x.header_offset = x.header_offset + concat
+            x.header_offset = x.header_offset + self._start_disk
             x.filename = x._decodeFilename()
             self.filelist.append(x)
             self.NameToInfo[x.filename] = x
@@ -1198,7 +1201,7 @@
                 raise RuntimeError('Compressed size larger than uncompressed size')
         # Seek backwards and write file header (which will now include
         # correct CRC and file sizes)
-        position = self.fp.tell()       # Preserve current position in file
+        position = self.fp.tell() # Preserve current position in file
         self.fp.seek(zinfo.header_offset, 0)
         self.fp.write(zinfo.FileHeader(zip64))
         self.fp.seek(position, 0)
@@ -1284,11 +1287,10 @@
                         file_size = zinfo.file_size
                         compress_size = zinfo.compress_size
 
-                    if zinfo.header_offset > ZIP64_LIMIT:
-                        extra.append(zinfo.header_offset)
+                    header_offset = zinfo.header_offset - self._start_disk
+                    if header_offset > ZIP64_LIMIT:
+                        extra.append(header_offset)
                         header_offset = 0xffffffffL
-                    else:
-                        header_offset = zinfo.header_offset
 
                     extra_data = zinfo.extra
                     if extra:
@@ -1332,7 +1334,7 @@
                 # Write end-of-zip-archive record
                 centDirCount = len(self.filelist)
                 centDirSize = pos2 - pos1
-                centDirOffset = pos1
+                centDirOffset = pos1 - self._start_disk
                 requires_zip64 = None
                 if centDirCount > ZIP_FILECOUNT_LIMIT:
                     requires_zip64 = "Files count"