diff --git a/src/allmydata/storage/http_server.py b/src/allmydata/storage/http_server.py
index 3ae16ae5c..7437b3ec7 100644
--- a/src/allmydata/storage/http_server.py
+++ b/src/allmydata/storage/http_server.py
@@ -4,7 +4,7 @@ HTTP server for storage.
 
 from __future__ import annotations
 
-from typing import Dict, List, Set, Tuple, Any, Callable, Union, cast
+from typing import Any, Callable, Union, cast
 from functools import wraps
 from base64 import b64decode
 import binascii
@@ -67,8 +67,8 @@ class ClientSecretsException(Exception):
 
 
 def _extract_secrets(
-    header_values, required_secrets
-):  # type: (List[str], Set[Secrets]) -> Dict[Secrets, bytes]
+    header_values: list[str], required_secrets: set[Secrets]
+) -> dict[Secrets, bytes]:
     """
     Given list of values of ``X-Tahoe-Authorization`` headers, and required
     secrets, return dictionary mapping secrets to decoded values.
@@ -173,7 +173,7 @@ class UploadsInProgress(object):
     _uploads: dict[bytes, StorageIndexUploads] = Factory(dict)
 
     # Map BucketWriter to (storage index, share number)
-    _bucketwriters: dict[BucketWriter, Tuple[bytes, int]] = Factory(dict)
+    _bucketwriters: dict[BucketWriter, tuple[bytes, int]] = Factory(dict)
 
     def add_write_bucket(
         self,
@@ -798,7 +798,9 @@ class HTTPServer(object):
         # The reason can be a string with explanation, so in theory it could be
         # longish?
         info = await self._read_encoded(
-            request, _SCHEMAS["advise_corrupt_share"], max_size=32768,
+            request,
+            _SCHEMAS["advise_corrupt_share"],
+            max_size=32768,
         )
         bucket.advise_corrupt_share(info["reason"].encode("utf-8"))
         return b""
@@ -973,7 +975,7 @@ def listen_tls(
     endpoint: IStreamServerEndpoint,
     private_key_path: FilePath,
     cert_path: FilePath,
-) -> Deferred[Tuple[DecodedURL, IListeningPort]]:
+) -> Deferred[tuple[DecodedURL, IListeningPort]]:
     """
     Start a HTTPS storage server on the given port, return the NURL and the
     listening port.