diff --git a/.github/workflows/famedly-tests.yml b/.github/workflows/famedly-tests.yml
index 8d55b50fca..6af8a86eb1 100644
--- a/.github/workflows/famedly-tests.yml
+++ b/.github/workflows/famedly-tests.yml
@@ -240,7 +240,11 @@ jobs:
         run: until pg_isready -h localhost; do sleep 1; done
       # coverage is already installed from the pyproject.toml file
       - run: poetry run pip install coverage-enable-subprocess
-      - run: poetry run coverage run -m twisted.trial -j6 tests
+        # Normally, this Github runner has 2 cores(actually threads) available to it.
+        # Using only one trial test runner does not saturate the cpu. Rough experimentation in the past led to having 3
+        # of these runners per core as optimal, but now coverage is required and there may be the need
+        # to scale back a little. This should be 6 trial test runners/jobs
+      - run: poetry run coverage run -m twisted.trial -j$((`nproc` * 3 )) tests
         env:
           SYNAPSE_POSTGRES: ${{ matrix.job.database == 'postgres' || '' }}
           SYNAPSE_POSTGRES_HOST: /var/run/postgresql
diff --git a/tests/handlers/test_worker_lock.py b/tests/handlers/test_worker_lock.py
index 6e9a15c8ee..d01641b297 100644
--- a/tests/handlers/test_worker_lock.py
+++ b/tests/handlers/test_worker_lock.py
@@ -54,8 +54,11 @@ def test_wait_for_lock_locally(self) -> None:
     def test_lock_contention(self) -> None:
         """Test lock contention when a lot of locks wait on a single worker"""
 
-        # It takes around 0.5s on a 5+ years old laptop
-        with test_timeout(5):
+        # It takes around 0.5s on a 5+ years old laptop when tests are not heavily
+        # concurrent. The database load(even with sqlite in memory) seems to hit a wall
+        # after `nproc` * 4 number of jobs. Increasing the timeout allows all the
+        # database reads/writes to actually complete
+        with test_timeout(15):
             nb_locks = 500
             d = self._take_locks(nb_locks)
             self.assertEqual(self.get_success(d), nb_locks)
diff --git a/tests/rest/admin/test_user.py b/tests/rest/admin/test_user.py
index a35a250975..35fda847cd 100644
--- a/tests/rest/admin/test_user.py
+++ b/tests/rest/admin/test_user.py
@@ -23,7 +23,6 @@
 import hmac
 import json
 import os
-import time
 import urllib.parse
 from binascii import unhexlify
 from http import HTTPStatus
@@ -5531,12 +5530,14 @@ def test_redact_messages_all_rooms(self) -> None:
         id = channel.json_body.get("redact_id")
 
         timeout_s = 10
-        start_time = time.time()
+        start_time = self.clock.time()
         redact_result = ""
         while redact_result != "complete":
-            if start_time + timeout_s < time.time():
+            if start_time + timeout_s < self.clock.time():
                 self.fail("Timed out waiting for redactions.")
 
+            # It's a background task, give it a shot at actually finishing
+            self.pump()
             channel2 = self.make_request(
                 "GET",
                 f"/_synapse/admin/v1/user/redact_status/{id}",