diff --git a/Lib/gzip.py b/Lib/gzip.py
index 6aacc9a..8fb1ed0 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -33,9 +33,6 @@
     # or unsigned.
     output.write(struct.pack("<L", value))
 
-def read32(input):
-    return struct.unpack("<I", input.read(4))[0]
-
 def open(filename, mode="rb", compresslevel=9):
     """Shorthand for GzipFile(filename, mode, compresslevel).
 
@@ -259,27 +256,31 @@
         self.crc = zlib.crc32(b"") & 0xffffffff
         self.size = 0
 
+    def _read_exact(self, n):
+        data = self.fileobj.read(n)
+        while len(data) < n:
+            b = self.fileobj.read(n - len(data))
+            if not b:
+                raise EOFError("Compressed file ended before the "
+                               "end-of-stream marker was reached")
+            data += b
+        return data
+
     def _read_gzip_header(self):
         magic = self.fileobj.read(2)
         if magic == b'':
-            raise EOFError("Reached EOF")
+            return False
 
         if magic != b'\037\213':
             raise IOError('Not a gzipped file')
-        method = ord( self.fileobj.read(1) )
+
+        method, flag, self.mtime = struct.unpack("<BBIxx", self._read_exact(8))
         if method != 8:
             raise IOError('Unknown compression method')
-        flag = ord( self.fileobj.read(1) )
-        self.mtime = read32(self.fileobj)
-        # extraflag = self.fileobj.read(1)
-        # os = self.fileobj.read(1)
-        self.fileobj.read(2)
 
         if flag & FEXTRA:
             # Read & discard the extra field, if present
-            xlen = ord(self.fileobj.read(1))
-            xlen = xlen + 256*ord(self.fileobj.read(1))
-            self.fileobj.read(xlen)
+            self._read_exact(struct.unpack("<H", self._read_exact(2)))
         if flag & FNAME:
             # Read and discard a null-terminated string containing the filename
             while True:
@@ -293,12 +294,13 @@
                 if not s or s==b'\000':
                     break
         if flag & FHCRC:
-            self.fileobj.read(2)     # Read & discard the 16-bit header CRC
+            self._read_exact(2)     # Read & discard the 16-bit header CRC
 
         unused = self.fileobj.unused()
         if unused:
             uncompress = self.decompress.decompress(unused)
             self._add_read_data(uncompress)
+        return True
 
     def write(self,data):
         self._check_closed()
@@ -332,20 +334,16 @@
 
         readsize = 1024
         if size < 0:        # get the whole thing
-            try:
-                while True:
-                    self._read(readsize)
-                    readsize = min(self.max_read_chunk, readsize * 2)
-            except EOFError:
-                size = self.extrasize
+            while self._read(readsize):
+                readsize = min(self.max_read_chunk, readsize * 2)
+            size = self.extrasize
         else:               # just get some more of it
-            try:
-                while size > self.extrasize:
-                    self._read(readsize)
-                    readsize = min(self.max_read_chunk, readsize * 2)
-            except EOFError:
-                if size > self.extrasize:
-                    size = self.extrasize
+            while size > self.extrasize:
+                if not self._read(readsize):
+                    if size > self.extrasize:
+                        size = self.extrasize
+                    break
+                readsize = min(self.max_read_chunk, readsize * 2)
 
         offset = self.offset - self.extrastart
         chunk = self.extrabuf[offset: offset + size]
@@ -366,12 +364,9 @@
         if self.extrasize == 0:
             if self.fileobj is None:
                 return b''
-            try:
-                # Ensure that we don't return b"" if we haven't reached EOF.
-                while self.extrasize == 0:
-                    # 1024 is the same buffering heuristic used in read()
-                    self._read(max(n, 1024))
-            except EOFError:
+            # Ensure that we don't return b"" if we haven't reached EOF.
+            # 1024 is the same buffering heuristic used in read()
+            while self.extrasize == 0 and self._read(max(n, 1024)):
                 pass
         offset = self.offset - self.extrastart
         remaining = self.extrasize
@@ -384,13 +379,14 @@
 
     def _read(self, size=1024):
         if self.fileobj is None:
-            raise EOFError("Reached EOF")
+            return False
 
         if self._new_member:
             # If the _new_member flag is set, we have to
             # jump to the next member, if there is one.
             self._init_read()
-            self._read_gzip_header()
+            if not self._read_gzip_header():
+                return False
             self.decompress = zlib.decompressobj(-zlib.MAX_WBITS)
             self._new_member = False
 
@@ -407,7 +403,7 @@
             self.fileobj.prepend(self.decompress.unused_data, True)
             self._read_eof()
             self._add_read_data( uncompress )
-            raise EOFError('Reached EOF')
+            return False
 
         uncompress = self.decompress.decompress(buf)
         self._add_read_data( uncompress )
@@ -423,6 +419,7 @@
             # a new member on the next call
             self._read_eof()
             self._new_member = True
+        return True
 
     def _add_read_data(self, data):
         self.crc = zlib.crc32(data, self.crc) & 0xffffffff
@@ -437,8 +434,7 @@
         # We check the that the computed CRC and size of the
         # uncompressed data matches the stored values.  Note that the size
         # stored is the true file size mod 2**32.
-        crc32 = read32(self.fileobj)
-        isize = read32(self.fileobj)  # may exceed 2GB
+        crc32, isize = struct.unpack("<II", self._read_exact(8))
         if crc32 != self.crc:
             raise IOError("CRC check failed %s != %s" % (hex(crc32),
                                                          hex(self.crc)))