diff --git a/pyop2/types/map.py b/pyop2/types/map.py
index 9d9ca48ae..81e386546 100644
--- a/pyop2/types/map.py
+++ b/pyop2/types/map.py
@@ -302,8 +302,6 @@ def __init__(self, maps):
         if self._initialized:
             return
         self._maps = maps
-        if not all(m is None or m.iterset == self.iterset for m in self._maps):
-            raise ex.MapTypeError("All maps in a MixedMap need to share the same iterset")
         # TODO: Think about different communicators on maps (c.f. MixedSet)
         # TODO: What if all maps are None?
         comms = tuple(m.comm for m in self._maps if m is not None)
@@ -344,7 +342,11 @@ def split(self):
     @utils.cached_property
     def iterset(self):
         """:class:`MixedSet` mapped from."""
-        return functools.reduce(lambda a, b: a or b, map(lambda s: s if s is None else s.iterset, self._maps))
+        s, = set(m.iterset for m in self._maps)
+        if len(s) == 1:
+            return functools.reduce(lambda a, b: a or b, map(lambda s: s if s is None else s.iterset, self._maps))
+        else:
+            raise RuntimeError("Found multiple itersets.")
 
     @utils.cached_property
     def toset(self):
@@ -356,7 +358,11 @@ def toset(self):
     def arity(self):
         """Arity of the mapping: total number of toset elements mapped to per
         iterset element."""
-        return sum(m.arity for m in self._maps)
+        s, = set(m.iterset for m in self._maps)
+        if len(s) == 1:
+            return sum(m.arity for m in self._maps)
+        else:
+            raise RuntimeError("Found multiple itersets.")
 
     @utils.cached_property
     def arities(self):
@@ -402,7 +408,7 @@ def offset(self):
     @utils.cached_property
     def offset_quotient(self):
         """Offsets quotient."""
-        raise NotImplementedError("offset_quotient not implemented for MixedMap")
+        return tuple(0 if m is None else m.offset_quotient for m in self._maps)
 
     def __iter__(self):
         r"""Yield all :class:`Map`\s when iterated over."""
diff --git a/pyop2/types/set.py b/pyop2/types/set.py
index 25abdf93c..62123f482 100644
--- a/pyop2/types/set.py
+++ b/pyop2/types/set.py
@@ -78,6 +78,10 @@ def __init__(self, size, name=None, halo=None, comm=None):
         # A cache of objects built on top of this set
         self._cache = {}
 
+    def indices(self):
+        """Returns iterator."""
+        return range(self.total_size)
+
     @utils.cached_property
     def core_size(self):
         """Core set size.  Owned elements not touching halo elements."""
diff --git a/test/unit/test_api.py b/test/unit/test_api.py
index 066d4aa9b..468d17558 100644
--- a/test/unit/test_api.py
+++ b/test/unit/test_api.py
@@ -1446,11 +1446,6 @@ def test_mixed_map_split(self, maps):
             assert mmap.split[i] == m
         assert mmap.split[:-1] == tuple(mmap)[:-1]
 
-    def test_mixed_map_nonunique_itset(self, m_iterset_toset, m_set_toset):
-        "Map toset should be Set."
-        with pytest.raises(exceptions.MapTypeError):
-            op2.MixedMap((m_iterset_toset, m_set_toset))
-
     def test_mixed_map_iterset(self, mmap):
         "MixedMap iterset should return the common iterset of all Maps."
         for m in mmap: