diff --git a/patoolib/__init__.py b/patoolib/__init__.py
index b032b40..1addcd5 100644
--- a/patoolib/__init__.py
+++ b/patoolib/__init__.py
@@ -283,10 +283,8 @@ def program_supports_compression (program, compression):
     @return: True iff the program supports the given compression format
       natively, else False.
     """
-    if program == 'py_tarfile':
+    if program in ('tar', 'star', 'py_tarfile'):
         return compression in ('gzip', 'bzip2')
-    if program in ('tar', 'star'):
-        return compression in ('gzip', 'bzip2', 'xz', 'lzma')
     return False