Issue #28449: tarfile.open() with mode "r" or "r:" now tries to open a tar
file with compression before trying to open it without compression.  Otherwise
it had 50% chance failed with ignore_zeros=True.
diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index be68800..adf91d5 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1665,7 +1665,9 @@
 
         if mode in ("r", "r:*"):
             # Find out which *open() is appropriate for opening the file.
-            for comptype in cls.OPEN_METH:
+            def not_compressed(comptype):
+                return cls.OPEN_METH[comptype] == 'taropen'
+            for comptype in sorted(cls.OPEN_METH, key=not_compressed):
                 func = getattr(cls, cls.OPEN_METH[comptype])
                 if fileobj is not None:
                     saved_pos = fileobj.tell()
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 3f9e996..89bd738 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -2,7 +2,9 @@
 import os
 import shutil
 import StringIO
+from binascii import unhexlify
 from hashlib import md5
+from random import Random
 import errno
 
 import unittest
@@ -276,12 +278,17 @@
         else:
             _open = open
 
+        # generate 512 pseudorandom bytes
+        data = unhexlify('%1024x' % Random(0).getrandbits(512*8))
         for char in ('\0', 'a'):
             # Test if EOFHeaderError ('\0') and InvalidHeaderError ('a')
             # are ignored correctly.
             with _open(tmpname, "wb") as fobj:
                 fobj.write(char * 1024)
-                fobj.write(tarfile.TarInfo("foo").tobuf())
+                tarinfo = tarfile.TarInfo("foo")
+                tarinfo.size = len(data)
+                fobj.write(tarinfo.tobuf())
+                fobj.write(data)
 
             tar = tarfile.open(tmpname, mode="r", ignore_zeros=True)
             try: