diff --git a/tests/storage/test_state.py b/tests/storage/test_state.py
index a433e7087063..bad7f0bc6026 100644
--- a/tests/storage/test_state.py
+++ b/tests/storage/test_state.py
@@ -26,7 +26,7 @@
 from synapse.types.state import StateFilter
 from synapse.util import Clock
 
-from tests.unittest import HomeserverTestCase, TestCase
+from tests.unittest import HomeserverTestCase
 
 logger = logging.getLogger(__name__)
 
@@ -494,624 +494,3 @@ def test_get_state_for_event(self) -> None:
 
         self.assertEqual(is_all, True)
         self.assertDictEqual({(e5.type, e5.state_key): e5.event_id}, state_dict)
-
-
-class StateFilterDifferenceTestCase(TestCase):
-    def assert_difference(
-        self, minuend: StateFilter, subtrahend: StateFilter, expected: StateFilter
-    ) -> None:
-        self.assertEqual(
-            minuend.approx_difference(subtrahend),
-            expected,
-            f"StateFilter difference not correct:\n\n\t{minuend!r}\nminus\n\t{subtrahend!r}\nwas\n\t{minuend.approx_difference(subtrahend)}\nexpected\n\t{expected}",
-        )
-
-    def test_state_filter_difference_no_include_other_minus_no_include_other(
-        self,
-    ) -> None:
-        """
-        Tests the StateFilter.approx_difference method
-        where, in a.approx_difference(b), both a and b do not have the
-        include_others flag set.
-        """
-        # (wildcard on state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.Create: None},
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
-                include_others=False,
-            ),
-            StateFilter.freeze({EventTypes.Create: None}, include_others=False),
-        )
-
-        # (wildcard on state keys) - (specific state keys)
-        # This one is an over-approximation because we can't represent
-        # 'all state keys except a few named examples'
-        self.assert_difference(
-            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
-            StateFilter.freeze(
-                {EventTypes.Member: {"@wombat:spqr"}},
-                include_others=False,
-            ),
-            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
-        )
-
-        # (wildcard on state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {EventTypes.CanonicalAlias: {""}},
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (specific state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr"},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-        )
-
-    def test_state_filter_difference_include_other_minus_no_include_other(self) -> None:
-        """
-        Tests the StateFilter.approx_difference method
-        where, in a.approx_difference(b), only a has the include_others flag set.
-        """
-        # (wildcard on state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.Create: None},
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Create: None,
-                    EventTypes.Member: set(),
-                    EventTypes.CanonicalAlias: set(),
-                },
-                include_others=True,
-            ),
-        )
-
-        # (wildcard on state keys) - (specific state keys)
-        # This one is an over-approximation because we can't represent
-        # 'all state keys except a few named examples'
-        # This also shows that the resultant state filter is normalised.
-        self.assert_difference(
-            StateFilter.freeze({EventTypes.Member: None}, include_others=True),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr"},
-                    EventTypes.Create: {""},
-                },
-                include_others=False,
-            ),
-            StateFilter(types=frozendict(), include_others=True),
-        )
-
-        # (wildcard on state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=False,
-            ),
-            StateFilter(
-                types=frozendict(),
-                include_others=True,
-            ),
-        )
-
-        # (specific state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.CanonicalAlias: {""},
-                    EventTypes.Member: set(),
-                },
-                include_others=True,
-            ),
-        )
-
-        # (specific state keys) - (specific state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr"},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-        )
-
-        # (specific state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-        )
-
-    def test_state_filter_difference_include_other_minus_include_other(self) -> None:
-        """
-        Tests the StateFilter.approx_difference method
-        where, in a.approx_difference(b), both a and b have the include_others
-        flag set.
-        """
-        # (wildcard on state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.Create: None},
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
-                include_others=True,
-            ),
-            StateFilter(types=frozendict(), include_others=False),
-        )
-
-        # (wildcard on state keys) - (specific state keys)
-        # This one is an over-approximation because we can't represent
-        # 'all state keys except a few named examples'
-        self.assert_difference(
-            StateFilter.freeze({EventTypes.Member: None}, include_others=True),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
-                include_others=False,
-            ),
-        )
-
-        # (wildcard on state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=True,
-            ),
-            StateFilter(
-                types=frozendict(),
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (specific state keys)
-        # This one is an over-approximation because we can't represent
-        # 'all state keys except a few named examples'
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                    EventTypes.Create: {""},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr"},
-                    EventTypes.Create: set(),
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@spqr:spqr"},
-                    EventTypes.Create: {""},
-                },
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                },
-                include_others=False,
-            ),
-        )
-
-    def test_state_filter_difference_no_include_other_minus_include_other(self) -> None:
-        """
-        Tests the StateFilter.approx_difference method
-        where, in a.approx_difference(b), only b has the include_others flag set.
-        """
-        # (wildcard on state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.Create: None},
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
-                include_others=True,
-            ),
-            StateFilter(types=frozendict(), include_others=False),
-        )
-
-        # (wildcard on state keys) - (specific state keys)
-        # This one is an over-approximation because we can't represent
-        # 'all state keys except a few named examples'
-        self.assert_difference(
-            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
-            StateFilter.freeze(
-                {EventTypes.Member: {"@wombat:spqr"}},
-                include_others=True,
-            ),
-            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
-        )
-
-        # (wildcard on state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (wildcard on state keys):
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=True,
-            ),
-            StateFilter(
-                types=frozendict(),
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (specific state keys)
-        # This one is an over-approximation because we can't represent
-        # 'all state keys except a few named examples'
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr"},
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@spqr:spqr"},
-                },
-                include_others=False,
-            ),
-        )
-
-        # (specific state keys) - (no state keys)
-        self.assert_difference(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                    EventTypes.CanonicalAlias: {""},
-                },
-                include_others=False,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: set(),
-                },
-                include_others=True,
-            ),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
-                },
-                include_others=False,
-            ),
-        )
-
-    def test_state_filter_difference_simple_cases(self) -> None:
-        """
-        Tests some very simple cases of the StateFilter approx_difference,
-        that are not explicitly tested by the more in-depth tests.
-        """
-
-        self.assert_difference(StateFilter.all(), StateFilter.all(), StateFilter.none())
-
-        self.assert_difference(
-            StateFilter.all(),
-            StateFilter.none(),
-            StateFilter.all(),
-        )
-
-
-class StateFilterTestCase(TestCase):
-    def test_return_expanded(self) -> None:
-        """
-        Tests the behaviour of the return_expanded() function that expands
-        StateFilters to include more state types (for the sake of cache hit rate).
-        """
-
-        self.assertEqual(StateFilter.all().return_expanded(), StateFilter.all())
-
-        self.assertEqual(StateFilter.none().return_expanded(), StateFilter.none())
-
-        # Concrete-only state filters stay the same
-        # (Case: mixed filter)
-        self.assertEqual(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
-                    "some.other.state.type": {""},
-                },
-                include_others=False,
-            ).return_expanded(),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
-                    "some.other.state.type": {""},
-                },
-                include_others=False,
-            ),
-        )
-
-        # Concrete-only state filters stay the same
-        # (Case: non-member-only filter)
-        self.assertEqual(
-            StateFilter.freeze(
-                {"some.other.state.type": {""}}, include_others=False
-            ).return_expanded(),
-            StateFilter.freeze({"some.other.state.type": {""}}, include_others=False),
-        )
-
-        # Concrete-only state filters stay the same
-        # (Case: member-only filter)
-        self.assertEqual(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
-                },
-                include_others=False,
-            ).return_expanded(),
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
-                },
-                include_others=False,
-            ),
-        )
-
-        # Wildcard member-only state filters stay the same
-        self.assertEqual(
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ).return_expanded(),
-            StateFilter.freeze(
-                {EventTypes.Member: None},
-                include_others=False,
-            ),
-        )
-
-        # If there is a wildcard in the non-member portion of the filter,
-        # it's expanded to include ALL non-member events.
-        # (Case: mixed filter)
-        self.assertEqual(
-            StateFilter.freeze(
-                {
-                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
-                    "some.other.state.type": None,
-                },
-                include_others=False,
-            ).return_expanded(),
-            StateFilter.freeze(
-                {EventTypes.Member: {"@wombat:test", "@alicia:test"}},
-                include_others=True,
-            ),
-        )
-
-        # If there is a wildcard in the non-member portion of the filter,
-        # it's expanded to include ALL non-member events.
-        # (Case: non-member-only filter)
-        self.assertEqual(
-            StateFilter.freeze(
-                {
-                    "some.other.state.type": None,
-                },
-                include_others=False,
-            ).return_expanded(),
-            StateFilter.freeze({EventTypes.Member: set()}, include_others=True),
-        )
-        self.assertEqual(
-            StateFilter.freeze(
-                {
-                    "some.other.state.type": None,
-                    "yet.another.state.type": {"wombat"},
-                },
-                include_others=False,
-            ).return_expanded(),
-            StateFilter.freeze({EventTypes.Member: set()}, include_others=True),
-        )
diff --git a/tests/types/__init__.py b/tests/types/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/tests/types/test_state.py b/tests/types/test_state.py
new file mode 100644
index 000000000000..eb809f9fb739
--- /dev/null
+++ b/tests/types/test_state.py
@@ -0,0 +1,627 @@
+from frozendict import frozendict
+
+from synapse.api.constants import EventTypes
+from synapse.types.state import StateFilter
+
+from tests.unittest import TestCase
+
+
+class StateFilterDifferenceTestCase(TestCase):
+    def assert_difference(
+        self, minuend: StateFilter, subtrahend: StateFilter, expected: StateFilter
+    ) -> None:
+        self.assertEqual(
+            minuend.approx_difference(subtrahend),
+            expected,
+            f"StateFilter difference not correct:\n\n\t{minuend!r}\nminus\n\t{subtrahend!r}\nwas\n\t{minuend.approx_difference(subtrahend)}\nexpected\n\t{expected}",
+        )
+
+    def test_state_filter_difference_no_include_other_minus_no_include_other(
+        self,
+    ) -> None:
+        """
+        Tests the StateFilter.approx_difference method
+        where, in a.approx_difference(b), both a and b do not have the
+        include_others flag set.
+        """
+        # (wildcard on state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.Create: None},
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
+                include_others=False,
+            ),
+            StateFilter.freeze({EventTypes.Create: None}, include_others=False),
+        )
+
+        # (wildcard on state keys) - (specific state keys)
+        # This one is an over-approximation because we can't represent
+        # 'all state keys except a few named examples'
+        self.assert_difference(
+            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
+            StateFilter.freeze(
+                {EventTypes.Member: {"@wombat:spqr"}},
+                include_others=False,
+            ),
+            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
+        )
+
+        # (wildcard on state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {EventTypes.CanonicalAlias: {""}},
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (specific state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr"},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+        )
+
+    def test_state_filter_difference_include_other_minus_no_include_other(self) -> None:
+        """
+        Tests the StateFilter.approx_difference method
+        where, in a.approx_difference(b), only a has the include_others flag set.
+        """
+        # (wildcard on state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.Create: None},
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Create: None,
+                    EventTypes.Member: set(),
+                    EventTypes.CanonicalAlias: set(),
+                },
+                include_others=True,
+            ),
+        )
+
+        # (wildcard on state keys) - (specific state keys)
+        # This one is an over-approximation because we can't represent
+        # 'all state keys except a few named examples'
+        # This also shows that the resultant state filter is normalised.
+        self.assert_difference(
+            StateFilter.freeze({EventTypes.Member: None}, include_others=True),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr"},
+                    EventTypes.Create: {""},
+                },
+                include_others=False,
+            ),
+            StateFilter(types=frozendict(), include_others=True),
+        )
+
+        # (wildcard on state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=False,
+            ),
+            StateFilter(
+                types=frozendict(),
+                include_others=True,
+            ),
+        )
+
+        # (specific state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.CanonicalAlias: {""},
+                    EventTypes.Member: set(),
+                },
+                include_others=True,
+            ),
+        )
+
+        # (specific state keys) - (specific state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr"},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+        )
+
+        # (specific state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+        )
+
+    def test_state_filter_difference_include_other_minus_include_other(self) -> None:
+        """
+        Tests the StateFilter.approx_difference method
+        where, in a.approx_difference(b), both a and b have the include_others
+        flag set.
+        """
+        # (wildcard on state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.Create: None},
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
+                include_others=True,
+            ),
+            StateFilter(types=frozendict(), include_others=False),
+        )
+
+        # (wildcard on state keys) - (specific state keys)
+        # This one is an over-approximation because we can't represent
+        # 'all state keys except a few named examples'
+        self.assert_difference(
+            StateFilter.freeze({EventTypes.Member: None}, include_others=True),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
+                include_others=False,
+            ),
+        )
+
+        # (wildcard on state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=True,
+            ),
+            StateFilter(
+                types=frozendict(),
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (specific state keys)
+        # This one is an over-approximation because we can't represent
+        # 'all state keys except a few named examples'
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                    EventTypes.Create: {""},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr"},
+                    EventTypes.Create: set(),
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@spqr:spqr"},
+                    EventTypes.Create: {""},
+                },
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                },
+                include_others=False,
+            ),
+        )
+
+    def test_state_filter_difference_no_include_other_minus_include_other(self) -> None:
+        """
+        Tests the StateFilter.approx_difference method
+        where, in a.approx_difference(b), only b has the include_others flag set.
+        """
+        # (wildcard on state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.Create: None},
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None, EventTypes.CanonicalAlias: None},
+                include_others=True,
+            ),
+            StateFilter(types=frozendict(), include_others=False),
+        )
+
+        # (wildcard on state keys) - (specific state keys)
+        # This one is an over-approximation because we can't represent
+        # 'all state keys except a few named examples'
+        self.assert_difference(
+            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
+            StateFilter.freeze(
+                {EventTypes.Member: {"@wombat:spqr"}},
+                include_others=True,
+            ),
+            StateFilter.freeze({EventTypes.Member: None}, include_others=False),
+        )
+
+        # (wildcard on state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (wildcard on state keys):
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=True,
+            ),
+            StateFilter(
+                types=frozendict(),
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (specific state keys)
+        # This one is an over-approximation because we can't represent
+        # 'all state keys except a few named examples'
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr"},
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@spqr:spqr"},
+                },
+                include_others=False,
+            ),
+        )
+
+        # (specific state keys) - (no state keys)
+        self.assert_difference(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                    EventTypes.CanonicalAlias: {""},
+                },
+                include_others=False,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: set(),
+                },
+                include_others=True,
+            ),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:spqr", "@spqr:spqr"},
+                },
+                include_others=False,
+            ),
+        )
+
+    def test_state_filter_difference_simple_cases(self) -> None:
+        """
+        Tests some very simple cases of the StateFilter approx_difference,
+        that are not explicitly tested by the more in-depth tests.
+        """
+
+        self.assert_difference(StateFilter.all(), StateFilter.all(), StateFilter.none())
+
+        self.assert_difference(
+            StateFilter.all(),
+            StateFilter.none(),
+            StateFilter.all(),
+        )
+
+
+class StateFilterTestCase(TestCase):
+    def test_return_expanded(self) -> None:
+        """
+        Tests the behaviour of the return_expanded() function that expands
+        StateFilters to include more state types (for the sake of cache hit rate).
+        """
+
+        self.assertEqual(StateFilter.all().return_expanded(), StateFilter.all())
+
+        self.assertEqual(StateFilter.none().return_expanded(), StateFilter.none())
+
+        # Concrete-only state filters stay the same
+        # (Case: mixed filter)
+        self.assertEqual(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
+                    "some.other.state.type": {""},
+                },
+                include_others=False,
+            ).return_expanded(),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
+                    "some.other.state.type": {""},
+                },
+                include_others=False,
+            ),
+        )
+
+        # Concrete-only state filters stay the same
+        # (Case: non-member-only filter)
+        self.assertEqual(
+            StateFilter.freeze(
+                {"some.other.state.type": {""}}, include_others=False
+            ).return_expanded(),
+            StateFilter.freeze({"some.other.state.type": {""}}, include_others=False),
+        )
+
+        # Concrete-only state filters stay the same
+        # (Case: member-only filter)
+        self.assertEqual(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
+                },
+                include_others=False,
+            ).return_expanded(),
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
+                },
+                include_others=False,
+            ),
+        )
+
+        # Wildcard member-only state filters stay the same
+        self.assertEqual(
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ).return_expanded(),
+            StateFilter.freeze(
+                {EventTypes.Member: None},
+                include_others=False,
+            ),
+        )
+
+        # If there is a wildcard in the non-member portion of the filter,
+        # it's expanded to include ALL non-member events.
+        # (Case: mixed filter)
+        self.assertEqual(
+            StateFilter.freeze(
+                {
+                    EventTypes.Member: {"@wombat:test", "@alicia:test"},
+                    "some.other.state.type": None,
+                },
+                include_others=False,
+            ).return_expanded(),
+            StateFilter.freeze(
+                {EventTypes.Member: {"@wombat:test", "@alicia:test"}},
+                include_others=True,
+            ),
+        )
+
+        # If there is a wildcard in the non-member portion of the filter,
+        # it's expanded to include ALL non-member events.
+        # (Case: non-member-only filter)
+        self.assertEqual(
+            StateFilter.freeze(
+                {
+                    "some.other.state.type": None,
+                },
+                include_others=False,
+            ).return_expanded(),
+            StateFilter.freeze({EventTypes.Member: set()}, include_others=True),
+        )
+        self.assertEqual(
+            StateFilter.freeze(
+                {
+                    "some.other.state.type": None,
+                    "yet.another.state.type": {"wombat"},
+                },
+                include_others=False,
+            ).return_expanded(),
+            StateFilter.freeze({EventTypes.Member: set()}, include_others=True),
+        )