diff --git a/tests/epics/adcore/test_drivers.py b/tests/epics/adcore/test_drivers.py
index 6d6cddd199..2fe67c3df5 100644
--- a/tests/epics/adcore/test_drivers.py
+++ b/tests/epics/adcore/test_drivers.py
@@ -70,7 +70,7 @@ async def test_start_acquiring_driver_and_ensure_status_flags_immediate_failure(
 ):
     set_mock_value(driver.detector_state, adcore.DetectorState.Error)
     acquiring = await adcore.start_acquiring_driver_and_ensure_status(
-        driver, timeout=0.01
+        driver, timeout=0.05
     )
     with pytest.raises(ValueError):
         await acquiring
diff --git a/tests/epics/demo/test_demo.py b/tests/epics/demo/test_demo.py
index e29e13bf29..7ab6c27d9b 100644
--- a/tests/epics/demo/test_demo.py
+++ b/tests/epics/demo/test_demo.py
@@ -19,13 +19,10 @@
     get_mock,
     get_mock_put,
     set_mock_value,
+    wait_for_pending_wakeups,
 )
 from ophyd_async.epics import demo
 
-# Long enough for multiple asyncio event loop cycles to run so
-# all the tasks have a chance to run
-A_WHILE = 0.001
-
 
 @pytest.fixture
 async def mock_mover() -> demo.Mover:
@@ -141,7 +138,7 @@ async def test_mover_moving_well(mock_mover: demo.Mover) -> None:
         time_elapsed=pytest.approx(0.1, abs=0.05),
     )
     set_mock_value(mock_mover.readback, 0.5499999)
-    await asyncio.sleep(A_WHILE)
+    await wait_for_pending_wakeups()
     assert s.done
     assert s.success
     done.assert_called_once_with(s)