diff --git a/python/src/docket/dependencies/_timeout.py b/python/src/docket/dependencies/_timeout.py
index a4416995..ab5b64cf 100644
--- a/python/src/docket/dependencies/_timeout.py
+++ b/python/src/docket/dependencies/_timeout.py
@@ -79,7 +79,7 @@ async def run(
 
         timed_out = False
         try:
-            while not task.done():  # pragma: no branch
+            while True:
                 if self.expired():
                     timed_out = True
                     break
@@ -89,6 +89,10 @@ async def run(
                         asyncio.shield(task), timeout=self.remaining().total_seconds()
                     )
                 except asyncio.TimeoutError:
+                    # Either the task raised TimeoutError itself, or it finished
+                    # as the deadline fired; report its own outcome.
+                    if task.done():
+                        return task.result()
                     continue
         finally:
             if not task.done():
diff --git a/python/tests/test_timeout_task_errors.py b/python/tests/test_timeout_task_errors.py
new file mode 100644
index 00000000..72b6a929
--- /dev/null
+++ b/python/tests/test_timeout_task_errors.py
@@ -0,0 +1,128 @@
+"""Tests for exceptions a task raises while a Timeout dependency runs it."""
+
+import asyncio
+import logging
+import traceback
+from datetime import timedelta
+
+import pytest
+
+from docket import Docket, Retry, Timeout, Worker
+from docket.execution import ExecutionState
+
+
+def error_logged(caplog: pytest.LogCaptureFixture, message: str) -> bool:
+    return any(
+        record.levelno == logging.ERROR
+        and record.exc_info is not None
+        and str(record.exc_info[1]) == message
+        for record in caplog.records
+    )
+
+
+@pytest.mark.parametrize("error_type", [ValueError, TimeoutError])
+async def test_an_error_from_the_task_body_fails_the_task(
+    docket: Docket,
+    worker: Worker,
+    caplog: pytest.LogCaptureFixture,
+    error_type: type[Exception],
+):
+    """A TimeoutError the task raises itself fails the task, the same as a ValueError."""
+
+    async def raises_its_own_error(
+        timeout: Timeout = Timeout(timedelta(seconds=5)),
+    ):
+        raise error_type("the task's own error")
+
+    execution = await docket.add(raises_its_own_error)()
+
+    with caplog.at_level(logging.ERROR):
+        await worker.run_until_finished()
+
+    await execution.sync()
+    assert execution.state == ExecutionState.FAILED
+    with pytest.raises(error_type, match="the task's own error"):
+        await execution.get_result()
+    assert error_logged(caplog, "the task's own error")
+
+
+async def test_a_wait_for_timeout_inside_the_task_fails_the_task(
+    docket: Docket, worker: Worker, caplog: pytest.LogCaptureFixture
+):
+    """A timed-out asyncio.wait_for inside the task fails the task with that error.
+
+    On Python 3.10, asyncio.TimeoutError is a separate class from the builtin
+    TimeoutError, so this covers the case the builtin TimeoutError test does not.
+    """
+
+    async def waits_too_long_for_something(
+        timeout: Timeout = Timeout(timedelta(seconds=5)),
+    ):
+        await asyncio.wait_for(asyncio.sleep(5), timeout=0.01)
+
+    execution = await docket.add(waits_too_long_for_something)()
+
+    with caplog.at_level(logging.ERROR):
+        await worker.run_until_finished()
+
+    await execution.sync()
+    assert execution.state == ExecutionState.FAILED
+    with pytest.raises(asyncio.TimeoutError) as raised:
+        await execution.get_result()
+    assert "exceeded timeout" not in str(raised.value)
+
+    logged_errors = [
+        record.exc_info[1]
+        for record in caplog.records
+        if record.levelno == logging.ERROR and record.exc_info is not None
+    ]
+    assert len(logged_errors) == 1
+    assert isinstance(logged_errors[0], asyncio.TimeoutError)
+    raising_frames = [
+        frame.f_code.co_name
+        for frame, _ in traceback.walk_tb(logged_errors[0].__traceback__)
+    ]
+    assert "waits_too_long_for_something" in raising_frames
+
+
+async def test_a_timeout_error_from_the_task_body_is_retried(
+    docket: Docket, worker: Worker
+):
+    """A task's own TimeoutError triggers its Retry, the same as any other failure."""
+
+    attempts: list[int] = []
+
+    async def raises_timeout_error(
+        retry: Retry = Retry(attempts=3),
+        timeout: Timeout = Timeout(timedelta(seconds=5)),
+    ):
+        attempts.append(retry.attempt)
+        raise TimeoutError("the task's own error")
+
+    await docket.add(raises_timeout_error)()
+
+    await worker.run_until_finished()
+
+    assert attempts == [1, 2, 3]
+
+
+async def test_overrunning_the_timeout_fails_the_task(
+    docket: Docket, worker: Worker, caplog: pytest.LogCaptureFixture
+):
+    """A task that runs past its Timeout is cancelled and fails with docket's timeout."""
+
+    async def runs_too_long(
+        timeout: Timeout = Timeout(timedelta(milliseconds=100)),
+    ):
+        await asyncio.sleep(5)
+
+    execution = await docket.add(runs_too_long)()
+
+    with caplog.at_level(logging.ERROR):
+        await worker.run_until_finished()
+
+    await execution.sync()
+    assert execution.state == ExecutionState.FAILED
+    with pytest.raises(asyncio.TimeoutError, match="exceeded timeout of 0.1s"):
+        await execution.get_result()
+    assert error_logged(caplog, f"Docket task {execution.key} exceeded timeout of 0.1s")