diff --git a/tests/storage/test_profile.py b/tests/storage/test_profile.py
index fe5bb7791336..bbe8bd88bc5b 100644
--- a/tests/storage/test_profile.py
+++ b/tests/storage/test_profile.py
@@ -15,8 +15,6 @@
 from twisted.test.proto_helpers import MemoryReactor
 
 from synapse.server import HomeServer
-from synapse.storage.database import LoggingTransaction
-from synapse.storage.engines import PostgresEngine
 from synapse.types import UserID
 from synapse.util import Clock
 
@@ -64,64 +62,3 @@ def test_avatar_url(self) -> None:
         self.assertIsNone(
             self.get_success(self.store.get_profile_avatar_url(self.u_frank))
         )
-
-    def test_profiles_bg_migration(self) -> None:
-        """
-        Test background job that copies entries from column user_id to full_user_id, adding
-        the hostname in the process.
-        """
-        updater = self.hs.get_datastores().main.db_pool.updates
-
-        # drop the constraint so we can insert nulls in full_user_id to populate the test
-        if isinstance(self.store.database_engine, PostgresEngine):
-
-            def f(txn: LoggingTransaction) -> None:
-                txn.execute(
-                    "ALTER TABLE profiles DROP CONSTRAINT full_user_id_not_null"
-                )
-
-            self.get_success(self.store.db_pool.runInteraction("", f))
-
-        for i in range(0, 70):
-            self.get_success(
-                self.store.db_pool.simple_insert(
-                    "profiles",
-                    {"user_id": f"hello{i:02}"},
-                )
-            )
-
-        # re-add the constraint so that when it's validated it actually exists
-        if isinstance(self.store.database_engine, PostgresEngine):
-
-            def f(txn: LoggingTransaction) -> None:
-                txn.execute(
-                    "ALTER TABLE profiles ADD CONSTRAINT full_user_id_not_null CHECK (full_user_id IS NOT NULL) NOT VALID"
-                )
-
-            self.get_success(self.store.db_pool.runInteraction("", f))
-
-        self.get_success(
-            self.store.db_pool.simple_insert(
-                "background_updates",
-                values={
-                    "update_name": "populate_full_user_id_profiles",
-                    "progress_json": "{}",
-                },
-            )
-        )
-
-        self.get_success(
-            updater.run_background_updates(False),
-        )
-
-        expected_values = []
-        for i in range(0, 70):
-            expected_values.append((f"@hello{i:02}:{self.hs.hostname}",))
-
-        res = self.get_success(
-            self.store.db_pool.execute(
-                "", None, "SELECT full_user_id from profiles ORDER BY full_user_id"
-            )
-        )
-        self.assertEqual(len(res), len(expected_values))
-        self.assertEqual(res, expected_values)
diff --git a/tests/storage/test_user_filters.py b/tests/storage/test_user_filters.py
deleted file mode 100644
index bab802f56ec6..000000000000
--- a/tests/storage/test_user_filters.py
+++ /dev/null
@@ -1,94 +0,0 @@
-# Copyright 2023 The Matrix.org Foundation C.I.C
-#
-# Licensed under the Apache License, Version 2.0 (the "License");
-# you may not use this file except in compliance with the License.
-# You may obtain a copy of the License at
-#
-#     http://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing, software
-# distributed under the License is distributed on an "AS IS" BASIS,
-# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-# See the License for the specific language governing permissions and
-# limitations under the License.
-
-
-from twisted.test.proto_helpers import MemoryReactor
-
-from synapse.server import HomeServer
-from synapse.storage.database import LoggingTransaction
-from synapse.storage.engines import PostgresEngine
-from synapse.util import Clock
-
-from tests import unittest
-
-
-class UserFiltersStoreTestCase(unittest.HomeserverTestCase):
-    """
-    Test background migration that copies entries from column user_id to full_user_id, adding
-    the hostname in the process.
-    """
-
-    def prepare(self, reactor: MemoryReactor, clock: Clock, hs: HomeServer) -> None:
-        self.store = hs.get_datastores().main
-
-    def test_bg_migration(self) -> None:
-        updater = self.hs.get_datastores().main.db_pool.updates
-
-        # drop the constraint so we can insert nulls in full_user_id to populate the test
-        if isinstance(self.store.database_engine, PostgresEngine):
-
-            def f(txn: LoggingTransaction) -> None:
-                txn.execute(
-                    "ALTER TABLE user_filters DROP CONSTRAINT full_user_id_not_null"
-                )
-
-            self.get_success(self.store.db_pool.runInteraction("", f))
-
-        for i in range(0, 70):
-            self.get_success(
-                self.store.db_pool.simple_insert(
-                    "user_filters",
-                    {
-                        "user_id": f"hello{i:02}",
-                        "filter_id": i,
-                        "filter_json": bytearray(i),
-                    },
-                )
-            )
-
-        # re-add the constraint so that when it's validated it actually exists
-        if isinstance(self.store.database_engine, PostgresEngine):
-
-            def f(txn: LoggingTransaction) -> None:
-                txn.execute(
-                    "ALTER TABLE user_filters ADD CONSTRAINT full_user_id_not_null CHECK (full_user_id IS NOT NULL) NOT VALID"
-                )
-
-            self.get_success(self.store.db_pool.runInteraction("", f))
-
-        self.get_success(
-            self.store.db_pool.simple_insert(
-                "background_updates",
-                values={
-                    "update_name": "populate_full_user_id_user_filters",
-                    "progress_json": "{}",
-                },
-            )
-        )
-
-        self.get_success(
-            updater.run_background_updates(False),
-        )
-
-        expected_values = []
-        for i in range(0, 70):
-            expected_values.append((f"@hello{i:02}:{self.hs.hostname}",))
-
-        res = self.get_success(
-            self.store.db_pool.execute(
-                "", None, "SELECT full_user_id from user_filters ORDER BY full_user_id"
-            )
-        )
-        self.assertEqual(len(res), len(expected_values))
-        self.assertEqual(res, expected_values)