diff --git a/src/runboat/models.py b/src/runboat/models.py
index 9c5d0fe..7a2c483 100644
--- a/src/runboat/models.py
+++ b/src/runboat/models.py
@@ -156,10 +156,10 @@ class Build(BaseModel):
     def live_link(self) -> str:
         return f"{self.webui_link}?live"
 
-    async def init_log(self) -> str:
+    async def init_log(self) -> str | None:
         return await k8s.log(self.name, job_kind=k8s.DeploymentMode.initialize)
 
-    async def log(self) -> str:
+    async def log(self) -> str | None:
         return await k8s.log(self.name, job_kind=None)
 
     @classmethod
diff --git a/src/runboat/utils.py b/src/runboat/utils.py
index 38ebd31..95f28cc 100644
--- a/src/runboat/utils.py
+++ b/src/runboat/utils.py
@@ -3,6 +3,16 @@ import functools
 import re
 from concurrent.futures.thread import ThreadPoolExecutor
 from functools import wraps
+from typing import (
+    Any,
+    AsyncGenerator,
+    Awaitable,
+    Callable,
+    Generator,
+    Iterator,
+    ParamSpec,
+    TypeVar,
+)
 
 _pool = ThreadPoolExecutor(max_workers=20, thread_name_prefix="sync_to_async")
 
@@ -11,29 +21,38 @@ def slugify(s: str | int) -> str:
     return re.sub(r"[^a-z0-9]", "-", str(s).lower())
 
 
-def sync_to_async(func):
+# TODO replace ... with P below when mypy supports PEP 612
+#      (https://github.com/python/mypy/issues/8645)
+P = ParamSpec("P")
+R = TypeVar("R")
+T = TypeVar("T")
+
+
+def sync_to_async(func: Callable[..., R]) -> Callable[..., Awaitable[R]]:
     @wraps(func)
-    async def inner(*args, **kwargs):
+    async def inner(*args: Any, **kwargs: Any) -> R:
         f = functools.partial(func, *args, **kwargs)
         return await asyncio.get_running_loop().run_in_executor(_pool, f)
 
     return inner
 
 
-def sync_to_async_iterator(iterator_func):
+def sync_to_async_iterator(
+    iterator_func: Callable[..., Generator[R, None, None]]
+) -> Callable[..., AsyncGenerator[R, None]]:
     @sync_to_async
-    def async_next(iterator):
+    def async_next(iterator: Iterator[R]) -> R:
         try:
             return next(iterator)
         except StopIteration:
             raise StopAsyncIteration()
 
     @sync_to_async
-    def async_iterator_func(*args, **kwargs):
+    def async_iterator_func(*args: Any, **kwargs: Any) -> Generator[R, None, None]:
         return iterator_func(*args, **kwargs)
 
     @wraps(iterator_func)
-    async def inner(*args, **kwargs):
+    async def inner(*args: Any, **kwargs: Any) -> AsyncGenerator[R, None]:
         iterator = await async_iterator_func(*args, **kwargs)
         while True:
             try: