diff --git a/src/allmydata/storage/http_client.py b/src/allmydata/storage/http_client.py
index 7fc68c902..b1877cd5f 100644
--- a/src/allmydata/storage/http_client.py
+++ b/src/allmydata/storage/http_client.py
@@ -5,7 +5,7 @@ HTTP client that talks to the HTTP storage server.
 from __future__ import annotations
 
 from eliot import start_action, register_exception_extractor
-from typing import Union, Optional, Sequence, Mapping, BinaryIO
+from typing import Union, Optional, Sequence, Mapping, BinaryIO, cast, TypedDict
 from base64 import b64encode
 from io import BytesIO
 from os import SEEK_END
@@ -486,13 +486,17 @@ class StorageClientGeneral(object):
         """
         url = self._client.relative_url("/storage/v1/version")
         response = await self._client.request("GET", url)
-        decoded_response = await self._client.decode_cbor(
-            response, _SCHEMAS["get_version"]
+        decoded_response = cast(
+            dict[bytes, object],
+            await self._client.decode_cbor(response, _SCHEMAS["get_version"]),
         )
         # Add some features we know are true because the HTTP API
         # specification requires them and because other parts of the storage
         # client implementation assumes they will be present.
-        decoded_response[b"http://allmydata.org/tahoe/protocols/storage/v1"].update(
+        cast(
+            dict[bytes, object],
+            decoded_response[b"http://allmydata.org/tahoe/protocols/storage/v1"],
+        ).update(
             {
                 b"tolerates-immutable-read-overrun": True,
                 b"delete-mutable-shares-with-zero-length-writev": True,
@@ -687,8 +691,9 @@ class StorageClientImmutables(object):
             upload_secret=upload_secret,
             message_to_serialize=message,
         )
-        decoded_response = await self._client.decode_cbor(
-            response, _SCHEMAS["allocate_buckets"]
+        decoded_response = cast(
+            dict[str, set[int]],
+            await self._client.decode_cbor(response, _SCHEMAS["allocate_buckets"]),
         )
         return ImmutableCreateResult(
             already_have=decoded_response["already-have"],
@@ -763,8 +768,11 @@ class StorageClientImmutables(object):
             raise ClientException(
                 response.code,
             )
-        body = await self._client.decode_cbor(
-            response, _SCHEMAS["immutable_write_share_chunk"]
+        body = cast(
+            dict[str, list[dict[str, int]]],
+            await self._client.decode_cbor(
+                response, _SCHEMAS["immutable_write_share_chunk"]
+            ),
         )
         remaining = RangeMap()
         for chunk in body["required"]:
@@ -794,7 +802,10 @@ class StorageClientImmutables(object):
             url,
         )
         if response.code == http.OK:
-            body = await self._client.decode_cbor(response, _SCHEMAS["list_shares"])
+            body = cast(
+                set[int],
+                await self._client.decode_cbor(response, _SCHEMAS["list_shares"]),
+            )
             return set(body)
         else:
             raise ClientException(response.code)
@@ -865,6 +876,12 @@ class ReadTestWriteResult:
     reads: Mapping[int, Sequence[bytes]]
 
 
+# Result type for mutable read/test/write HTTP response.
+MUTABLE_RTW = TypedDict(
+    "MUTABLE_RTW", {"success": bool, "data": dict[int, list[bytes]]}
+)
+
+
 @frozen
 class StorageClientMutables:
     """
@@ -911,8 +928,11 @@ class StorageClientMutables:
             message_to_serialize=message,
         )
         if response.code == http.OK:
-            result = await self._client.decode_cbor(
-                response, _SCHEMAS["mutable_read_test_write"]
+            result = cast(
+                MUTABLE_RTW,
+                await self._client.decode_cbor(
+                    response, _SCHEMAS["mutable_read_test_write"]
+                ),
             )
             return ReadTestWriteResult(success=result["success"], reads=result["data"])
         else:
@@ -942,8 +962,11 @@ class StorageClientMutables:
         )
         response = await self._client.request("GET", url)
         if response.code == http.OK:
-            return await self._client.decode_cbor(
-                response, _SCHEMAS["mutable_list_shares"]
+            return cast(
+                set[int],
+                await self._client.decode_cbor(
+                    response, _SCHEMAS["mutable_list_shares"]
+                ),
             )
         else:
             raise ClientException(response.code)