diff --git a/Lib/shutil.py b/Lib/shutil.py
index 99e4017..6d80fee 100644
--- a/Lib/shutil.py
+++ b/Lib/shutil.py
@@ -405,8 +405,10 @@
             except os.error:
                 onerror(os.unlink, fullname, sys.exc_info())
 
-_use_fd_functions = (os.unlink in os.supports_dir_fd and
-                     os.open in os.supports_dir_fd)
+_use_fd_functions = ({os.open, os.stat, os.unlink, os.rmdir} <=
+                     os.supports_dir_fd and
+                     os.listdir in os.supports_fd and
+                     os.stat in os.supports_follow_symlinks)
 
 def rmtree(path, ignore_errors=False, onerror=None):
     """Recursively delete a directory tree.
diff --git a/Lib/test/test_shutil.py b/Lib/test/test_shutil.py
index cb712b3..a2b6e88 100644
--- a/Lib/test/test_shutil.py
+++ b/Lib/test/test_shutil.py
@@ -524,7 +524,11 @@
         self.assertFalse(os.path.islink(dst))
 
     def test_rmtree_uses_safe_fd_version_if_available(self):
-        if os.unlink in os.supports_dir_fd and os.open in os.supports_dir_fd:
+        _use_fd_functions = ({os.open, os.stat, os.unlink, os.rmdir} <=
+                             os.supports_dir_fd and
+                             os.listdir in os.supports_fd and
+                             os.stat in os.supports_follow_symlinks)
+        if _use_fd_functions:
             self.assertTrue(shutil._use_fd_functions)
             self.assertTrue(shutil.rmtree.avoids_symlink_attacks)
             tmp_dir = self.mkdtemp()