diff --git a/tests/test_concurrency.py b/tests/test_concurrency.py
index 5a27e1904..9b15c8a65 100644
--- a/tests/test_concurrency.py
+++ b/tests/test_concurrency.py
@@ -1,4 +1,3 @@
-import asyncio
 import contextlib
 import time
 from collections.abc import Iterator
@@ -38,6 +37,7 @@ async def test_contextmanager_in_threadpool() -> None:
 
 
 @pytest.mark.anyio
+@pytest.mark.timeout(10, func_only=True)
 @pytest.mark.usefixtures("reset_teardown_limiter")
 async def test_competing_acquire_release() -> None:
     """Check that the main threadpool does not block the teardown threadpool."""
@@ -64,8 +64,6 @@ async def test_competing_acquire_release() -> None:
 
         # The threadpool should now be full of threads waiting to acquire
         # The release function should be able to run without being blocked by acquires
-        await asyncio.wait_for(
-            concurrency.run_in_teardown_threadpool(release), timeout=10
-        )
+        await concurrency.run_in_teardown_threadpool(release)
 
     assert len(acquired) == pool_size
diff --git a/tests/test_depends_deadlock.py b/tests/test_depends_deadlock.py
index 76e44cf68..bf9d4da9f 100644
--- a/tests/test_depends_deadlock.py
+++ b/tests/test_depends_deadlock.py
@@ -3,6 +3,7 @@ import threading
 import time
 from collections.abc import Iterator
 
+import pytest
 from fastapi import Depends, FastAPI
 from httpx import ASGITransport, AsyncClient
 from pydantic import BaseModel
@@ -42,6 +43,7 @@ def get_deadlock(dep: None = Depends(release_resource)) -> Item:
 # Fire off 100 requests in parallel(ish) in order to create contention
 # over the shared resource (simulating a fastapi server that interacts with
 # a database connection pool).
+@pytest.mark.timeout(10, func_only=True)
 def test_depends_deadlock() -> None:
     async def make_request(client: AsyncClient):
         await client.get("/deadlock")
@@ -53,4 +55,4 @@ def test_depends_deadlock() -> None:
             tasks = [make_request(aclient) for _ in range(100)]
             await asyncio.gather(*tasks)
 
-    asyncio.run(asyncio.wait_for(run_requests(), timeout=10))
+    asyncio.run(run_requests())