diff --git a/Lib/gzip.py b/Lib/gzip.py
index 55d448dd1d7..8802adb0d9a 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -15,12 +15,21 @@ FTEXT, FHCRC, FEXTRA, FNAME, FCOMMENT = 1, 2, 4, 8, 16
 
 READ, WRITE = 1, 2
 
+def U32(i):
+    """Return i as an unsigned integer, assuming it fits in 32 bits.
+
+    If it's >= 2GB when viewed as a 32-bit unsigned int, return a long.
+    """
+    if i < 0:
+        i += 1L << 32
+    return i
+
 def write32(output, value):
     output.write(struct.pack("<l", value))
 
 def write32u(output, value):
-    if value < 0:
-        value = value + 0x100000000L
+    # The L format writes the bit pattern correctly whether signed
+    # or unsigned.
     output.write(struct.pack("<L", value))
 
 def read32(input):
@@ -157,19 +166,21 @@ class GzipFile:
 
         if flag & FEXTRA:
             # Read & discard the extra field, if present
-            xlen=ord(self.fileobj.read(1))
-            xlen=xlen+256*ord(self.fileobj.read(1))
+            xlen = ord(self.fileobj.read(1))
+            xlen = xlen + 256*ord(self.fileobj.read(1))
             self.fileobj.read(xlen)
         if flag & FNAME:
             # Read and discard a null-terminated string containing the filename
             while True:
-                s=self.fileobj.read(1)
-                if not s or s=='\000': break
+                s = self.fileobj.read(1)
+                if not s or s=='\000':
+                    break
         if flag & FCOMMENT:
             # Read and discard a null-terminated string containing a comment
             while True:
-                s=self.fileobj.read(1)
-                if not s or s=='\000': break
+                s = self.fileobj.read(1)
+                if not s or s=='\000':
+                    break
         if flag & FHCRC:
             self.fileobj.read(2)     # Read & discard the 16-bit header CRC
 
@@ -225,7 +236,8 @@ class GzipFile:
         self.offset -= len(buf)
 
     def _read(self, size=1024):
-        if self.fileobj is None: raise EOFError, "Reached EOF"
+        if self.fileobj is None:
+            raise EOFError, "Reached EOF"
 
         if self._new_member:
             # If the _new_member flag is set, we have to
@@ -286,8 +298,8 @@ class GzipFile:
         # uncompressed data matches the stored values.
         self.fileobj.seek(-8, 1)
         crc32 = read32(self.fileobj)
-        isize = read32(self.fileobj)
-        if crc32%0x100000000L != self.crc%0x100000000L:
+        isize = U32(read32(self.fileobj))   # may exceed 2GB
+        if U32(crc32) != U32(self.crc):
             raise ValueError, "CRC check failed"
         elif isize != self.size:
             raise ValueError, "Incorrect length of data produced"
@@ -296,7 +308,8 @@ class GzipFile:
         if self.mode == WRITE:
             self.fileobj.write(self.compress.flush())
             write32(self.fileobj, self.crc)
-            write32(self.fileobj, self.size)
+            # self.size may exceed 2GB
+            write32u(self.fileobj, self.size)
             self.fileobj = None
         elif self.mode == READ:
             self.fileobj = None
@@ -338,15 +351,16 @@ class GzipFile:
             if offset < self.offset:
                 raise IOError('Negative seek in write mode')
             count = offset - self.offset
-            for i in range(count/1024):
-                self.write(1024*'\0')
-            self.write((count%1024)*'\0')
+            for i in range(count // 1024):
+                self.write(1024 * '\0')
+            self.write((count % 1024) * '\0')
         elif self.mode == READ:
             if offset < self.offset:
                 # for negative seek, rewind and do positive seek
                 self.rewind()
             count = offset - self.offset
-            for i in range(count/1024): self.read(1024)
+            for i in range(count // 1024):
+                self.read(1024)
             self.read(count % 1024)
 
     def readline(self, size=-1):
@@ -379,11 +393,13 @@ class GzipFile:
 
     def readlines(self, sizehint=0):
         # Negative numbers result in reading all the lines
-        if sizehint <= 0: sizehint = sys.maxint
+        if sizehint <= 0:
+            sizehint = sys.maxint
         L = []
         while sizehint > 0:
             line = self.readline()
-            if line == "": break
+            if line == "":
+                break
             L.append(line)
             sizehint = sizehint - len(line)
 
diff --git a/Misc/NEWS b/Misc/NEWS
index c8334d70c4e..980e4d2ec34 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -355,6 +355,10 @@ Extension modules
 Library
 -------
 
+- gzip.py now handles files exceeding 2GB.  Note that 4GB is still a
+  fundamental limitation of the underlying gzip file format (it only
+  has 32 bits to record the file size).
+
 - xml.sax.saxutils.unescape has been added, to replace entity references
   with their entity value.
 
@@ -365,7 +369,7 @@ Library
 
 - Various configure methods of Tkinter have been stream-lined, so that
   tag_configure, image_configure, window_configure now return a
-  dictionary when invoked with no argument. 
+  dictionary when invoked with no argument.
 
 - Importing the readline module now no longer has the side effect of
   calling setlocale(LC_CTYPE, "").  The initial "C" locale, or