diff --git a/tests/test_concurrency.py b/tests/test_concurrency.py
index 9b15c8a65..755bcbbf7 100644
--- a/tests/test_concurrency.py
+++ b/tests/test_concurrency.py
@@ -37,7 +37,6 @@ 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."""
@@ -46,15 +45,19 @@ async def test_competing_acquire_release() -> None:
     acquired = []
 
     def acquire() -> None:
-        while not acquirable:
+        # We wait a max of 5s to acquire, which should be more than enough
+        for _ in range(5000):
+            if acquirable:
+                break
             time.sleep(0.001)
+
+        assert acquirable, "Failed to acquire resource within timeout"
         acquired.append(True)
 
-    def release() -> bool:
+    def release() -> None:
         nonlocal acquirable
         time.sleep(0.001)
         acquirable = True
-        return acquirable
 
     async with anyio.create_task_group() as tg:
         for _ in range(pool_size):
diff --git a/tests/test_depends_deadlock.py b/tests/test_depends_deadlock.py
index bf9d4da9f..07e1a6303 100644
--- a/tests/test_depends_deadlock.py
+++ b/tests/test_depends_deadlock.py
@@ -1,4 +1,5 @@
 import asyncio
+import multiprocessing
 import threading
 import time
 from collections.abc import Iterator
@@ -40,11 +41,30 @@ def get_deadlock(dep: None = Depends(release_resource)) -> Item:
     return Item(name="foo", id=1)
 
 
+# NOTE: the failure mode here can cause the test suite to hang.
+# Since the default threadpool is a global which is not easily patched
+# (and doing so would make the test somewhat fragile/pointless)
+# we need to use a subprocess to isolate the bad behaviour.
+# If you are struggling to debug, comment out this function and rename
+# the impl_ version to test_depends_deadlock
+def test_depends_deadlock() -> None:
+
+    proc = multiprocessing.Process(target=impl_test_depends_deadlock, daemon=True)
+    proc.start()
+    proc.join(timeout=10)
+
+    try:
+        assert not proc.is_alive(), "Process is still alive after timeout, likely due to a deadlock"
+    finally:
+        proc.kill()  # Ensure the process is terminated if it's still alive
+
+    assert proc.exitcode == 0, "Process did not exit cleanly, see logs for details"
+
+
 # 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:
+def impl_test_depends_deadlock() -> None:
     async def make_request(client: AsyncClient):
         await client.get("/deadlock")