python
diff --git a/Lib/test/test_xxlimited.py b/Lib/test/test_xxlimited.py
@@ -1,19 +1,39 @@
 import unittest
 from test.support import import_helper
-import types
 
 xxlimited = import_helper.import_module('xxlimited')
-xxlimited_35 = import_helper.import_module('xxlimited_35')
 
-
-class CommonTests:
-    module: types.ModuleType
-
-    def test_xxo_new(self):
-        xxo = self.module.Xxo()
-
-    def test_xxo_attributes(self):
-        xxo = self.module.Xxo()
+# if import of xxlimited succeeded, the other ones should be importable.
+import xxlimited_3_13
+import xxlimited_35
+
+MODULES = {
+    (3, 15): xxlimited,
+    (3, 13): xxlimited_3_13,
+    (3, 5): xxlimited_35,
+}
+
+def test_with_xxlimited_modules(since=None, until=None):
+    def _decorator(func):
+        def _wrapper(self, *args, **kwargs):
+            for version, module in MODULES.items():
+                if since and version < since:
+                    continue
+                if until and version >= until:
+                    continue
+                with self.subTest(version=version):
+                    func(self, module, *args, **kwargs)
+        return _wrapper
+    return _decorator
+
+class XXLimitedTests(unittest.TestCase):
+    @test_with_xxlimited_modules()
+    def test_xxo_new(self, module):
+        xxo = module.Xxo()
+
+    @test_with_xxlimited_modules()
+    def test_xxo_attributes(self, module):
+        xxo = module.Xxo()
         with self.assertRaises(AttributeError):
             xxo.foo
         with self.assertRaises(AttributeError):
@@ -26,40 +46,61 @@ def test_xxo_attributes(self):
         with self.assertRaises(AttributeError):
             xxo.foo
 
-    def test_foo(self):
+    @test_with_xxlimited_modules()
+    def test_foo(self, module):
         # the foo function adds 2 numbers
-        self.assertEqual(self.module.foo(1, 2), 3)
+        self.assertEqual(module.foo(1, 2), 3)
 
-    def test_str(self):
-        self.assertIsSubclass(self.module.Str, str)
-        self.assertIsNot(self.module.Str, str)
+    @test_with_xxlimited_modules()
+    def test_str(self, module):
+        self.assertIsSubclass(module.Str, str)
+        self.assertIsNot(module.Str, str)
 
-        custom_string = self.module.Str("abcd")
+        custom_string = module.Str("abcd")
         self.assertEqual(custom_string, "abcd")
         self.assertEqual(custom_string.upper(), "ABCD")
 
-    def test_new(self):
-        xxo = self.module.new()
+    @test_with_xxlimited_modules()
+    def test_new(self, module):
+        xxo = module.new()
         self.assertEqual(xxo.demo("abc"), "abc")
 
-
-class TestXXLimited(CommonTests, unittest.TestCase):
-    module = xxlimited
-
-    def test_xxo_demo(self):
-        xxo = self.module.Xxo()
-        other = self.module.Xxo()
+    @test_with_xxlimited_modules()
+    def test_xxo_demo(self, module):
+        xxo = module.Xxo()
         self.assertEqual(xxo.demo("abc"), "abc")
+        self.assertEqual(xxo.demo(0), None)
+        self.assertEqual(xxo.__module__, module.__name__)
+        with self.assertRaises(TypeError):
+            module.Xxo('arg')
+        with self.assertRaises(TypeError):
+            module.Xxo(kwarg='arg')
+
+    @test_with_xxlimited_modules(since=(3, 13))
+    def test_xxo_demo_extra(self, module):
+        xxo = module.Xxo()
+        other = module.Xxo()
         self.assertEqual(xxo.demo(xxo), xxo)
         self.assertEqual(xxo.demo(other), other)
-        self.assertEqual(xxo.demo(0), None)
 
-    def test_error(self):
-        with self.assertRaises(self.module.Error):
-            raise self.module.Error
-
-    def test_buffer(self):
-        xxo = self.module.Xxo()
+    @test_with_xxlimited_modules(since=(3, 15))
+    def test_xxo_subclass(self, module):
+        class Sub(module.Xxo):
+            pass
+        sub = Sub()
+        sub.a = 123
+        self.assertEqual(sub.a, 123)
+        with self.assertRaisesRegex(AttributeError, "cannot set 'reserved'"):
+            sub.reserved = 123
+
+    @test_with_xxlimited_modules(since=(3, 13))
+    def test_error(self, module):
+        with self.assertRaises(module.Error):
+            raise module.Error
+
+    @test_with_xxlimited_modules(since=(3, 13))
+    def test_buffer(self, module):
+        xxo = module.Xxo()
         self.assertEqual(xxo.x_exports, 0)
         b1 = memoryview(xxo)
         self.assertEqual(xxo.x_exports, 1)
@@ -69,21 +110,13 @@ def test_buffer(self):
         self.assertEqual(b1[0], 1)
         self.assertEqual(b2[0], 1)
 
-
-class TestXXLimited35(CommonTests, unittest.TestCase):
-    module = xxlimited_35
-
-    def test_xxo_demo(self):
-        xxo = self.module.Xxo()
-        other = self.module.Xxo()
-        self.assertEqual(xxo.demo("abc"), "abc")
-        self.assertEqual(xxo.demo(0), None)
-
+    @test_with_xxlimited_modules(until=(3, 5))
     def test_roj(self):
         # the roj function always fails
         with self.assertRaises(SystemError):
             self.module.roj(0)
 
+    @test_with_xxlimited_modules(until=(3, 5))
     def test_null(self):
         null1 = self.module.Null()
         null2 = self.module.Null()

@@ -273,6 +273,7 @@ PYTHONPATH=$(COREPYTHONPATH)
 #xx xxmodule.c
 #xxlimited xxlimited.c
 #xxlimited_35 xxlimited_35.c
+#xxlimited_3_13 xxlimited_3_13.c
 #xxsubtype xxsubtype.c
 
 # Testing

@@ -190,6 +190,7 @@
 # Limited API template modules; must be built as shared modules.
 @MODULE_XXLIMITED_TRUE@xxlimited xxlimited.c
 @MODULE_XXLIMITED_35_TRUE@xxlimited_35 xxlimited_35.c
+@MODULE_XXLIMITED_3_13_TRUE@xxlimited_3_13 xxlimited_3_13.c
 
 
 # for performance