diff --git a/patoolib/programs/star.py b/patoolib/programs/star.py
index e7ca5c9..5b3abbf 100644
--- a/patoolib/programs/star.py
+++ b/patoolib/programs/star.py
@@ -48,5 +48,8 @@ def add_star_opts (cmdlist, encoding, verbose):
         cmdlist.append('-Z')
     elif encoding == 'bzip2':
         cmdlist.append('-bz')
+    elif encoding in ('lzma', 'xz'):
+        # use compress-program option
+        cmdlist.append('compress-program=%s' % encoding)
     if verbose:
         cmdlist.append('-v')
diff --git a/tests/test_archives.py b/tests/test_archives.py
index 3b8eb7c..2d9348e 100644
--- a/tests/test_archives.py
+++ b/tests/test_archives.py
@@ -31,8 +31,8 @@ class TestArchives (ArchiveTest):
         self.archive_commands('t.tar.Z', cmd)
         self.archive_commands('t.tar.bz2', cmd)
         self.archive_commands('t.tbz2', cmd)
-        # XXXself.archive_commands('t.tar.lzma', cmd)
-        # XXXself.archive_command('t.tar.xz', cmd)
+        self.archive_commands('t.tar.lzma', cmd)
+        self.archive_commands('t.tar.xz', cmd)
 
     @needs_cmd('bzip2')
     def test_bzip2 (self):