diff --git a/tests/components/hassio/test_handler.py b/tests/components/hassio/test_handler.py
index 5a89ea8335a91e..d92a5335809766 100644
--- a/tests/components/hassio/test_handler.py
+++ b/tests/components/hassio/test_handler.py
@@ -320,8 +320,8 @@ async def test_api_ingress_panels(
     ],
 )
 async def test_api_headers(
+    aiohttp_raw_server,  # 'aiohttp_raw_server' must be before 'hass'!
     hass,
-    aiohttp_raw_server,
     socket_enabled,
     api_call: str,
     method: Literal["GET", "POST"],
diff --git a/tests/helpers/test_script.py b/tests/helpers/test_script.py
index 5163dd0ca6d5a1..8e4409daa547de 100644
--- a/tests/helpers/test_script.py
+++ b/tests/helpers/test_script.py
@@ -1053,6 +1053,7 @@ async def test_multiple_runs_wait(hass: HomeAssistant, action_type) -> None:
         hass.states.async_set("switch.test", "on")
         hass.async_create_task(script_obj.async_run(context=Context()))
         await asyncio.wait_for(wait_started_flag.wait(), 1)
+        await asyncio.sleep(0)
 
         assert script_obj.is_running
         assert len(events) == 1
@@ -1062,6 +1063,7 @@ async def test_multiple_runs_wait(hass: HomeAssistant, action_type) -> None:
         wait_started_flag.clear()
         hass.async_create_task(script_obj.async_run())
         await asyncio.wait_for(wait_started_flag.wait(), 1)
+        await asyncio.sleep(0)
     except (AssertionError, asyncio.TimeoutError):
         await script_obj.async_stop()
         raise
@@ -4079,6 +4081,7 @@ async def test_script_mode_2(
         hass.states.async_set("switch.test", "on")
         hass.async_create_task(script_obj.async_run(context=Context()))
         await asyncio.wait_for(wait_started_flag.wait(), 1)
+        await asyncio.sleep(0)
 
         assert script_obj.is_running
         assert len(events) == 1
@@ -4089,6 +4092,7 @@ async def test_script_mode_2(
         wait_started_flag.clear()
         hass.async_create_task(script_obj.async_run(context=Context()))
         await asyncio.wait_for(wait_started_flag.wait(), 1)
+        await asyncio.sleep(0)
 
         assert script_obj.is_running
         assert len(events) == 2