diff --git a/tests/test_annotations.py b/tests/test_annotations.py
index 49c9b0d7b..049f5e992 100644
--- a/tests/test_annotations.py
+++ b/tests/test_annotations.py
@@ -94,6 +94,10 @@ class C:
         assert 1 == len(attr.fields(C))
         assert_init_annotations(C, x=typing.List[int])
 
+    @pytest.mark.skipif(
+        sys.version_info[:2] < (3, 11),
+        reason="Incompatible behavior on older Pythons",
+    )
     @pytest.mark.parametrize("slots", [True, False])
     def test_auto_attribs(self, slots):
         """
@@ -149,7 +153,7 @@ class C:
             x=typing.List[int],
             y=int,
             z=int,
-            foo=typing.Optional[typing.Any],
+            foo=typing.Any,
         )
 
     @pytest.mark.parametrize("slots", [True, False])
@@ -384,8 +388,9 @@ def noop():
 
         assert attr.converters.optional(noop).__annotations__ == {}
 
-    @pytest.mark.xfail(
-        sys.version_info[:2] == (3, 6), reason="Does not work on 3.6."
+    @pytest.mark.skipif(
+        sys.version_info[:2] < (3, 11),
+        reason="Incompatible behavior on older Pythons",
     )
     @pytest.mark.parametrize("slots", [True, False])
     def test_annotations_strings(self, slots):
@@ -417,7 +422,7 @@ class C:
             x=typing.List[int],
             y=int,
             z=int,
-            foo=typing.Optional[typing.Any],
+            foo=typing.Any,
         )
 
     @pytest.mark.parametrize("slots", [True, False])
diff --git a/tests/test_make.py b/tests/test_make.py
index d4d8640cd..96e07f333 100644
--- a/tests/test_make.py
+++ b/tests/test_make.py
@@ -2275,7 +2275,9 @@ class C:
             def __getstate__(self):
                 return ("hi",)
 
-        assert None is getattr(C(), "__setstate__", None)
+        assert getattr(object, "__setstate__", None) is getattr(
+            C, "__setstate__", None
+        )
 
         @attr.s(slots=slots, auto_detect=True)
         class C:
@@ -2291,7 +2293,9 @@ def __setstate__(self, state):
         i.__setstate__(())
 
         assert True is i.called
-        assert None is getattr(C(), "__getstate__", None)
+        assert getattr(object, "__getstate__", None) is getattr(
+            C, "__getstate__", None
+        )
 
     @pytest.mark.skipif(PY310, reason="Pre-3.10 only.")
     def test_match_args_pre_310(self):
diff --git a/tests/test_slots.py b/tests/test_slots.py
index 5f08d4cd1..de4e90e0b 100644
--- a/tests/test_slots.py
+++ b/tests/test_slots.py
@@ -660,10 +660,12 @@ def test_no_getstate_setstate_for_dict_classes(self):
         As long as getstate_setstate is None, nothing is done to dict
         classes.
         """
-        i = C1(1, 2)
-
-        assert None is getattr(i, "__getstate__", None)
-        assert None is getattr(i, "__setstate__", None)
+        assert getattr(object, "__getstate__", None) is getattr(
+            C1, "__getstate__", None
+        )
+        assert getattr(object, "__setstate__", None) is getattr(
+            C1, "__setstate__", None
+        )
 
     def test_no_getstate_setstate_if_option_false(self):
         """
@@ -674,10 +676,12 @@ def test_no_getstate_setstate_if_option_false(self):
         class C:
             x = attr.ib()
 
-        i = C(42)
-
-        assert None is getattr(i, "__getstate__", None)
-        assert None is getattr(i, "__setstate__", None)
+        assert getattr(object, "__getstate__", None) is getattr(
+            C, "__getstate__", None
+        )
+        assert getattr(object, "__setstate__", None) is getattr(
+            C, "__setstate__", None
+        )
 
     @pytest.mark.parametrize("cls", [C2(1), C2Slots(1)])
     def test_getstate_set_state_force_true(self, cls):