diff --git a/pottery/__init__.py b/pottery/__init__.py
index b7e94834..c64ae901 100644
--- a/pottery/__init__.py
+++ b/pottery/__init__.py
@@ -32,7 +32,7 @@
 
 
 __title__: Final[str] = 'pottery'
-__version__: Final[str] = '2.3.6'
+__version__: Final[str] = '2.3.7'
 __description__: Final[str] = __doc__.split(sep='\n\n', maxsplit=1)[0]
 __url__: Final[str] = 'https://github.com/brainix/pottery'
 __author__: Final[str] = 'Rajiv Bakulesh Shah'
diff --git a/pottery/bloom.py b/pottery/bloom.py
index b95a1ed5..7b7ad7a1 100644
--- a/pottery/bloom.py
+++ b/pottery/bloom.py
@@ -34,8 +34,8 @@
 from typing_extensions import final
 
 from .annotations import F
+from .annotations import JSONTypes
 from .base import Container
-from .base import JSONTypes
 
 
 # TODO: When we drop support for Python 3.7, stop using @_store_on_self().  Use
diff --git a/pottery/cache.py b/pottery/cache.py
index 7e42f560..f9f31e2b 100644
--- a/pottery/cache.py
+++ b/pottery/cache.py
@@ -29,8 +29,11 @@
 from typing import Collection
 from typing import Hashable
 from typing import Iterable
+from typing import Mapping
 from typing import NamedTuple
+from typing import Tuple
 from typing import TypeVar
+from typing import Union
 from typing import cast
 
 from redis import Redis
@@ -39,15 +42,20 @@
 #   from typing import Final
 from typing_extensions import Final
 
-from .base import JSONTypes
+from .annotations import JSONTypes
 from .base import _default_redis
 from .base import logger
 from .base import random_key
-from .dict import InitArg
-from .dict import InitIter
 from .dict import RedisDict
 
 
+F = TypeVar('F', bound=Callable[..., JSONTypes])
+
+UpdateMap = Mapping[JSONTypes, Union[JSONTypes, object]]
+UpdateItem = Tuple[JSONTypes, Union[JSONTypes, object]]
+UpdateIter = Iterable[UpdateItem]
+UpdateArg = Union[UpdateMap, UpdateIter]
+
 _DEFAULT_TIMEOUT: Final[int] = 60   # seconds
 
 
@@ -68,9 +76,6 @@ def _arg_hash(*args: Hashable, **kwargs: Hashable) -> int:
     return hash((args, kwargs_items))
 
 
-F = TypeVar('F', bound=Callable[..., JSONTypes])
-
-
 def redis_cache(*,  # NoQA: C901
                 redis: Redis | None = None,
                 key: str | None = None,
@@ -248,13 +253,14 @@ def __init__(self,
             )
             for dict_key, encoded_value in zip(dict_keys, encoded_values):
                 if encoded_value is None:
-                    value = self._SENTINEL
                     self._misses.add(dict_key)
+                    value = self._SENTINEL
                 else:
                     value = self._cache._decode(encoded_value)
                 item = (dict_key, value)
                 items.append(item)
-        return super().__init__(items)
+        super().__init__()
+        self.__update(items)
 
     def misses(self) -> Collection[JSONTypes]:
         return frozenset(self._misses)
@@ -265,7 +271,7 @@ def __setitem__(self,
                     value: JSONTypes | object,
                     ) -> None:
         'Set self[dict_key] to value.'
-        if value is not self._SENTINEL:
+        if value is not self._SENTINEL:  # pragma: no cover
             self._cache[dict_key] = value
             self._misses.discard(dict_key)
         return super().__setitem__(dict_key, value)
@@ -318,24 +324,29 @@ def __retry(self, callable: Callable[[], Any], *, try_num: int = 0) -> Any:
             raise
 
     @_set_expiration
-    def update(self, arg: InitArg = tuple(), **kwargs: JSONTypes) -> None:  # type: ignore
+    def update(self,  # type: ignore
+               arg: UpdateArg = tuple(),
+               **kwargs: JSONTypes | object,
+               ) -> None:
         '''D.update([E, ]**F) -> None.  Update D from dict/iterable E and F.
         If E is present and has an .items() method, then does:  for k in E: D[k] = E[k]
         If E is present and lacks an .items() method, then does:  for k, v in E: D[k] = v
         In either case, this is followed by: for k in F:  D[k] = F[k]
 
         The base class, OrderedDict, has an .update() method that works just
-        fine.  The trouble is that it executes multiple calls to .__setitem__()
-        therefore multiple round trips to Redis.  This overridden .update()
-        makes a single bulk call to Redis.
+        fine.  The trouble is that it executes multiple calls to
+        self.__setitem__() therefore multiple round trips to Redis.  This
+        overridden .update() makes a single bulk call to Redis.
         '''
         to_cache = {}
         if isinstance(arg, collections.abc.Mapping):
             arg = arg.items()
-        items = itertools.chain(cast(InitIter, arg), kwargs.items())
+        items = itertools.chain(arg, kwargs.items())
         for dict_key, value in items:
             if value is not self._SENTINEL:
                 to_cache[dict_key] = value
-                self._misses.discard(dict_key)
+                self._misses.discard(cast(JSONTypes, dict_key))
             super().__setitem__(dict_key, value)
         self._cache.update(to_cache)
+
+    __update = update
diff --git a/pottery/counter.py b/pottery/counter.py
index 70bc6d80..72324dcc 100644
--- a/pottery/counter.py
+++ b/pottery/counter.py
@@ -36,7 +36,7 @@
 from redis.client import Pipeline
 from typing_extensions import Counter
 
-from .base import JSONTypes
+from .annotations import JSONTypes
 from .dict import RedisDict
 
 
diff --git a/pottery/deque.py b/pottery/deque.py
index 5cf052f7..6df1160d 100644
--- a/pottery/deque.py
+++ b/pottery/deque.py
@@ -29,7 +29,7 @@
 from redis import Redis
 from redis.client import Pipeline
 
-from .base import JSONTypes
+from .annotations import JSONTypes
 from .exceptions import InefficientAccessWarning
 from .list import RedisList
 
diff --git a/pottery/dict.py b/pottery/dict.py
index 0833523e..508b44c7 100644
--- a/pottery/dict.py
+++ b/pottery/dict.py
@@ -35,9 +35,9 @@
 from redis import Redis
 from redis.client import Pipeline
 
+from .annotations import JSONTypes
 from .base import Container
 from .base import Iterable_
-from .base import JSONTypes
 from .exceptions import InefficientAccessWarning
 from .exceptions import KeyExistsError
 
diff --git a/pottery/hyper.py b/pottery/hyper.py
index 59a51d21..c28ee6f9 100644
--- a/pottery/hyper.py
+++ b/pottery/hyper.py
@@ -31,9 +31,9 @@
 
 from redis import Redis
 
+from .annotations import JSONTypes
 from .annotations import RedisValues
 from .base import Container
-from .base import JSONTypes
 from .base import random_key
 
 
diff --git a/pottery/list.py b/pottery/list.py
index b834094a..1267d137 100644
--- a/pottery/list.py
+++ b/pottery/list.py
@@ -42,8 +42,8 @@
 from typing_extensions import final
 
 from .annotations import F
+from .annotations import JSONTypes
 from .base import Container
-from .base import JSONTypes
 from .exceptions import InefficientAccessWarning
 from .exceptions import KeyExistsError
 
diff --git a/pottery/queue.py b/pottery/queue.py
index 57be8fbf..48adb93e 100644
--- a/pottery/queue.py
+++ b/pottery/queue.py
@@ -29,8 +29,8 @@
 
 from redis import WatchError
 
+from .annotations import JSONTypes
 from .base import Container
-from .base import JSONTypes
 from .exceptions import QueueEmptyError
 from .timer import ContextTimer
 
diff --git a/pottery/set.py b/pottery/set.py
index bd712c44..ce897a12 100644
--- a/pottery/set.py
+++ b/pottery/set.py
@@ -35,9 +35,9 @@
 from redis.client import Pipeline
 from typing_extensions import Literal
 
+from .annotations import JSONTypes
 from .base import Container
 from .base import Iterable_
-from .base import JSONTypes
 from .exceptions import InefficientAccessWarning
 from .exceptions import KeyExistsError