diff --git a/src/cachetools/__init__.py b/src/cachetools/__init__.py
index 54baa46a..ca67c588 100644
--- a/src/cachetools/__init__.py
+++ b/src/cachetools/__init__.py
@@ -16,7 +16,7 @@ __all__ = (
     'cached', 'cachedmethod'
 )
 
-__version__ = '2.0.1'
+__version__ = '2.1.0'
 
 if hasattr(functools.update_wrapper(lambda f: f(), lambda: 42), '__wrapped__'):
     _update_wrapper = functools.update_wrapper
diff --git a/src/cachetools/abc.py b/src/cachetools/abc.py
index d265f633..b663d96e 100644
--- a/src/cachetools/abc.py
+++ b/src/cachetools/abc.py
@@ -1,7 +1,6 @@
 from __future__ import absolute_import
 
 import collections
-
 from abc import abstractmethod
 
 
diff --git a/src/cachetools/cache.py b/src/cachetools/cache.py
index 08526311..a9a3e571 100644
--- a/src/cachetools/cache.py
+++ b/src/cachetools/cache.py
@@ -1,5 +1,7 @@
 from __future__ import absolute_import
 
+from warnings import warn
+
 from .abc import DefaultMapping
 
 
@@ -14,16 +16,23 @@ class _DefaultSize(object):
         return 1
 
 
+_deprecated = object()
+
+
 class Cache(DefaultMapping):
     """Mutable mapping to serve as a simple cache or cache base class."""
 
     __size = _DefaultSize()
 
-    def __init__(self, maxsize, missing=None, getsizeof=None):
-        if missing:
-            self.__missing = missing
+    def __init__(self, maxsize, missing=_deprecated, getsizeof=None):
+        if missing is not _deprecated:
+            warn("Cache constructor parameter 'missing' is deprecated",
+                 DeprecationWarning, 3)
+            if missing:
+                self.__missing = missing
         if getsizeof:
-            self.__getsizeof = getsizeof
+            self.getsizeof = getsizeof
+        if self.getsizeof is not Cache.getsizeof:
             self.__size = dict()
         self.__data = dict()
         self.__currsize = 0
@@ -81,14 +90,6 @@ class Cache(DefaultMapping):
     def __len__(self):
         return len(self.__data)
 
-    @staticmethod
-    def __getsizeof(value):
-        return 1
-
-    @staticmethod
-    def __missing(key):
-        raise KeyError(key)
-
     @property
     def maxsize(self):
         """The maximum size of the cache."""
@@ -99,6 +100,11 @@ class Cache(DefaultMapping):
         """The current size of the cache."""
         return self.__currsize
 
-    def getsizeof(self, value):
+    @staticmethod
+    def getsizeof(value):
         """Return the size of a cache element's value."""
-        return self.__getsizeof(value)
+        return 1
+
+    @staticmethod
+    def __missing(key):
+        raise KeyError(key)
diff --git a/src/cachetools/lfu.py b/src/cachetools/lfu.py
index f5817a43..76a264a6 100644
--- a/src/cachetools/lfu.py
+++ b/src/cachetools/lfu.py
@@ -2,13 +2,13 @@ from __future__ import absolute_import
 
 import collections
 
-from .cache import Cache
+from .cache import Cache, _deprecated
 
 
 class LFUCache(Cache):
     """Least Frequently Used (LFU) cache implementation."""
 
-    def __init__(self, maxsize, missing=None, getsizeof=None):
+    def __init__(self, maxsize, missing=_deprecated, getsizeof=None):
         Cache.__init__(self, maxsize, missing, getsizeof)
         self.__counter = collections.Counter()
 
diff --git a/src/cachetools/lru.py b/src/cachetools/lru.py
index b945797c..991b0e23 100644
--- a/src/cachetools/lru.py
+++ b/src/cachetools/lru.py
@@ -2,13 +2,13 @@ from __future__ import absolute_import
 
 import collections
 
-from .cache import Cache
+from .cache import Cache, _deprecated
 
 
 class LRUCache(Cache):
     """Least Recently Used (LRU) cache implementation."""
 
-    def __init__(self, maxsize, missing=None, getsizeof=None):
+    def __init__(self, maxsize, missing=_deprecated, getsizeof=None):
         Cache.__init__(self, maxsize, missing, getsizeof)
         self.__order = collections.OrderedDict()
 
diff --git a/src/cachetools/rr.py b/src/cachetools/rr.py
index 8cd856c3..1aeed438 100644
--- a/src/cachetools/rr.py
+++ b/src/cachetools/rr.py
@@ -2,16 +2,25 @@ from __future__ import absolute_import
 
 import random
 
-from .cache import Cache
+from .cache import Cache, _deprecated
+
+
+# random.choice cannot be pickled in Python 2.7
+def _choice(seq):
+    return random.choice(seq)
 
 
 class RRCache(Cache):
     """Random Replacement (RR) cache implementation."""
 
-    def __init__(self, maxsize, choice=random.choice, missing=None,
+    def __init__(self, maxsize, choice=random.choice, missing=_deprecated,
                  getsizeof=None):
         Cache.__init__(self, maxsize, missing, getsizeof)
-        self.__choice = choice
+        # TODO: use None as default, assing to self.choice directly?
+        if choice is random.choice:
+            self.__choice = _choice
+        else:
+            self.__choice = choice
 
     @property
     def choice(self):
diff --git a/src/cachetools/ttl.py b/src/cachetools/ttl.py
index d20cc0b2..d4c3b37b 100644
--- a/src/cachetools/ttl.py
+++ b/src/cachetools/ttl.py
@@ -3,7 +3,7 @@ from __future__ import absolute_import
 import collections
 import time
 
-from .cache import Cache
+from .cache import Cache, _deprecated
 
 
 class _Link(object):
@@ -57,7 +57,7 @@ class _Timer(object):
 class TTLCache(Cache):
     """LRU Cache implementation with per-item time-to-live (TTL) value."""
 
-    def __init__(self, maxsize, ttl, timer=time.time, missing=None,
+    def __init__(self, maxsize, ttl, timer=time.time, missing=_deprecated,
                  getsizeof=None):
         Cache.__init__(self, maxsize, missing, getsizeof)
         self.__root = root = _Link()