diff --git a/devito/tools/data_structures.py b/devito/tools/data_structures.py
index 95bafe87a35..207e71fa207 100644
--- a/devito/tools/data_structures.py
+++ b/devito/tools/data_structures.py
@@ -38,20 +38,17 @@ def __iter__(self):
 
 
 class EnrichedTuple(tuple, Pickable):
-
     """
     A tuple with an arbitrary number of additional attributes.
     """
 
-    __rargs__ = ('*values',)
+    __rargs__ = ('*items',)
     __rkwargs__ = ('getters',)
 
     def __new__(cls, *items, getters=None, **kwargs):
         obj = super().__new__(cls, items)
         obj.__dict__.update(kwargs)
-        if getters is not None or '_getters' not in kwargs:
-            # Don't override _getters if getters=None
-            obj._getters = OrderedDict(zip(getters or (), items))
+        obj._getters = OrderedDict(zip(getters or [], items))
         return obj
 
     def __getitem__(self, key):
@@ -76,15 +73,18 @@ def __getitem_hook__(self, key):
     def __getnewargs_ex__(self):
         # Bypass default reconstruction logic since this class spawns
         # objects with varying number of attributes
-        return (tuple(self), dict(self.__dict__))
+        kwargs = dict(self.__dict__)
+        kwargs['getters'] = list(kwargs.pop('_getters', []))
+
+        return tuple(self), kwargs
 
     def get(self, key, val=None):
         return self._getters.get(key, val)
 
     @property
-    def values(self) -> tuple:
+    def items(self) -> tuple:
         # Needed for rargs
-        return self
+        return tuple(self)
 
     @cached_property
     def getters(self) -> tuple:
diff --git a/devito/types/utils.py b/devito/types/utils.py
index 59e61374227..d1409ddcccd 100644
--- a/devito/types/utils.py
+++ b/devito/types/utils.py
@@ -24,6 +24,12 @@ class Stagger(Tag):
 
 class DimensionTuple(EnrichedTuple):
 
+    __rkwargs__ = EnrichedTuple.__rkwargs__ + ('left', 'right')
+
+    def __new__(cls, *args, getters=None, left=None, right=None, **kwargs):
+        return super().__new__(cls, *args, getters=getters,
+                               left=left, right=right, **kwargs)
+
     def __getitem_hook__(self, dim):
         for d in self._getters:
             if d._defines & dim._defines: