diff --git a/SimPEG/Maps.py b/SimPEG/Maps.py
index 00f8f302..dde3e752 100644
--- a/SimPEG/Maps.py
+++ b/SimPEG/Maps.py
@@ -1,7 +1,7 @@
 import Utils, Parameters, numpy as np, scipy.sparse as sp
 from Tests import checkDerivative
 
-class BaseModel(object):
+class IdentityMap(object):
     """
     SimPEG Model
 
@@ -66,9 +66,14 @@ class BaseModel(object):
                 kwargs['plotIt'] = False
         return checkDerivative(lambda m : [self.transform(m), self.transformDeriv(m)], m, **kwargs)
 
-class BaseNonLinearModel(object):
+    def _assertMatchesPair(self, pair):
+        assert (isinstance(self, pair) or
+            isinstance(self, ComboMap) and isinstance(self.models[0], pair)
+            ), "Model object must be an instance of a %s class."%(pair.__name__)
+
+class NonLinearMap(object):
     """
-    SimPEG BaseNonLinearModel
+    SimPEG NonLinearMap
 
     """
 
@@ -129,11 +134,11 @@ class BaseNonLinearModel(object):
         raise NotImplementedError('The test is not implemented.')
 
 
-class LogModel(BaseModel):
-    """SimPEG LogModel"""
+class ExpMap(IdentityMap):
+    """SimPEG ExpMap"""
 
     def __init__(self, mesh, **kwargs):
-        BaseModel.__init__(self, mesh, **kwargs)
+        IdentityMap.__init__(self, mesh, **kwargs)
 
     def transform(self, m):
         """
@@ -197,8 +202,8 @@ class LogModel(BaseModel):
         """
         return Utils.sdiag(np.exp(Utils.mkvc(m)))
 
-class Vertical1DModel(BaseModel):
-    """Vertical1DModel
+class Vertical1DMap(IdentityMap):
+    """Vertical1DMap
 
         Given a 1D vector through the last dimension
         of the mesh, this will extend to the full
@@ -206,7 +211,7 @@ class Vertical1DModel(BaseModel):
     """
 
     def __init__(self, mesh, **kwargs):
-        BaseModel.__init__(self, mesh, **kwargs)
+        IdentityMap.__init__(self, mesh, **kwargs)
 
     @property
     def nP(self):
@@ -238,7 +243,7 @@ class Vertical1DModel(BaseModel):
                     ), shape=(repNum, 1))
         return sp.kron(sp.identity(self.nP), repVec)
 
-class Mesh2Mesh(BaseModel):
+class Mesh2Mesh(IdentityMap):
     """
         Takes a model on one mesh are translates it to another mesh.
 
@@ -251,8 +256,8 @@ class Mesh2Mesh(BaseModel):
             M2 = Mesh.TensorMesh([h1,h1])
             V = Utils.ModelBuilder.randomModel(M.vnC, seed=79, its=50)
             v = Utils.mkvc(V)
-            modh = Model.Mesh2Mesh([M,M2])
-            modH = Model.Mesh2Mesh([M2,M])
+            modh = Maps.Mesh2Mesh([M,M2])
+            modH = Maps.Mesh2Mesh([M2,M])
             H = modH.transform(v)
             h = modh.transform(H)
             ax = plt.subplot(131)
@@ -289,7 +294,7 @@ class Mesh2Mesh(BaseModel):
         return self.P
 
 
-class ActiveModel(BaseModel):
+class ActiveCells(IdentityMap):
     """
         Active model parameters.
 
@@ -329,15 +334,15 @@ class ActiveModel(BaseModel):
     def transformDeriv(self, m):
         return self.P
 
-class ComboModel(BaseModel):
+class ComboMap(IdentityMap):
     """Combination of various models."""
 
     def __init__(self, mesh, models, **kwargs):
-        BaseModel.__init__(self, mesh, **kwargs)
+        IdentityMap.__init__(self, mesh, **kwargs)
 
         self.models = []
         for m in models:
-            if not isinstance(m, BaseModel):
+            if not isinstance(m, IdentityMap):
                 self.models += [m(mesh, **kwargs)]
             else:
                 self.models += [m]
@@ -366,7 +371,7 @@ class ComboModel(BaseModel):
 if __name__ == '__main__':
     from SimPEG import *
     mesh = Mesh.TensorMesh([10,8])
-    combo = ComboModel(mesh, [LogModel, Vertical1DModel])
+    combo = ComboMap(mesh, [ExpMap, Vertical1DMap])
     m = combo.example()
     print m.shape
     print combo.test(np.arange(8))
diff --git a/SimPEG/Problem.py b/SimPEG/Problem.py
index 477ba604..7e6ba0d7 100644
--- a/SimPEG/Problem.py
+++ b/SimPEG/Problem.py
@@ -1,5 +1,5 @@
 import Utils, Survey, numpy as np, scipy.sparse as sp
-import Model
+import Maps
 
 class BaseProblem(object):
     """
@@ -11,19 +11,16 @@ class BaseProblem(object):
     counter = None   #: A SimPEG.Utils.Counter object
 
     surveyPair = Survey.BaseSurvey   #: A SimPEG.Survey Class
-    modelPair = Model.BaseModel  #: A SimPEG.Model Class
+    mapPair    = Maps.IdentityMap    #: A SimPEG.Map Class
 
-    def __init__(self, model, **kwargs):
+    mapping = None    #: A SimPEG.Map instance.
+    mesh    = None    #: A SimPEG.Mesh instance.
+
+    def __init__(self, mesh, mapping=None, **kwargs):
         Utils.setKwargs(self, **kwargs)
-        assert (isinstance(model, self.modelPair) or
-            isinstance(model, Model.ComboModel) and isinstance(model.models[0], self.modelPair)
-            ), "Model object must be an instance of a %s class."%(self.modelPair.__name__)
-        self.model = model
-
-    @property
-    def mesh(self):
-        """SimPEG mesh that is associated with the model provided."""
-        return self.model.mesh
+        self.mesh = mesh
+        self.mapping = mapping or Maps.IdentityMap(mesh)
+        self.mapping._assertMatchesPair(mapPair)
 
     @property
     def survey(self):
diff --git a/SimPEG/Regularization.py b/SimPEG/Regularization.py
index 8f7b9ede..cc78df36 100644
--- a/SimPEG/Regularization.py
+++ b/SimPEG/Regularization.py
@@ -1,4 +1,4 @@
-import Utils, Model, Parameters, numpy as np, scipy.sparse as sp
+import Utils, Maps, Parameters, numpy as np, scipy.sparse as sp
 
 class BaseRegularization(object):
     """
@@ -12,16 +12,20 @@ class BaseRegularization(object):
 
     __metaclass__ = Utils.SimPEGMetaClass
 
-    modelPair = Model.BaseModel  #: Some regularizations only work on specific models
 
-    model = None    #: A SimPEG.Model instance.
 
     counter = None
 
-    def __init__(self, model, **kwargs):
+    mapPair = Maps.IdentityMap    #: A SimPEG.Map Class
+
+    mapping = None    #: A SimPEG.Map instance.
+    mesh    = None    #: A SimPEG.Mesh instance.
+
+    def __init__(self, mesh, mapping=None, **kwargs):
         Utils.setKwargs(self, **kwargs)
-        assert isinstance(model, self.modelPair), "Incorrect model for this regularization"
-        self.model = model
+        self.mesh = mesh
+        self.mapping = mapping or Maps.IdentityMap(mesh)
+        self.mapping._assertMatchesPair(mapPair)
 
     mref = Parameters.ParameterProperty('mref', default=None, doc='Reference model.')
 
@@ -47,8 +51,6 @@ class BaseRegularization(object):
     def prob(self): return self.parent.prob
     @property
     def survey(self): return self.parent.survey
-    @property
-    def mesh(self): return self.model.mesh
 
 
     @property
@@ -59,7 +61,7 @@ class BaseRegularization(object):
 
     @Utils.timeIt
     def modelObj(self, m):
-        r = self.W * self.model.transform(m - self.mref)
+        r = self.W * self.mapping.transform(m - self.mref)
         return 0.5*r.dot(r)
 
     @Utils.timeIt
@@ -79,8 +81,8 @@ class BaseRegularization(object):
             R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
 
         """
-        mTd = self.model.transformDeriv(m - self.mref)
-        return mTd.T * ( self.W.T * ( self.W * self.model.transform(m - self.mref) ) )
+        mTd = self.mapping.transformDeriv(m - self.mref)
+        return mTd.T * ( self.W.T * ( self.W * self.mapping.transform(m - self.mref) ) )
 
     @Utils.timeIt
     def modelObj2Deriv(self, m, v=None):
@@ -104,7 +106,7 @@ class BaseRegularization(object):
             R(m) = \mathbf{W^\\top W}
 
         """
-        mTd = self.model.transformDeriv(m - self.mref)
+        mTd = self.mapping.transformDeriv(m - self.mref)
         if v is None:
             return mTd.T * self.W.T * self.W * mTd
 
diff --git a/SimPEG/Tests/test_model.py b/SimPEG/Tests/test_maps.py
similarity index 61%
rename from SimPEG/Tests/test_model.py
rename to SimPEG/Tests/test_maps.py
index cd4a0e07..abd5701f 100644
--- a/SimPEG/Tests/test_model.py
+++ b/SimPEG/Tests/test_maps.py
@@ -5,7 +5,7 @@ from TestUtils import checkDerivative
 from scipy.sparse.linalg import dsolve
 
 
-class ModelTests(unittest.TestCase):
+class MapTests(unittest.TestCase):
 
     def setUp(self):
 
@@ -15,22 +15,22 @@ class ModelTests(unittest.TestCase):
         self.mesh22 = Mesh.TensorMesh([b, a], x0=np.array([3, 5]))
 
     def test_modelTransforms(self):
-        for M in dir(Model):
+        for M in dir(Maps):
             try:
-                model = getattr(Model, M)(self.mesh2)
-                assert isinstance(model, Model.BaseModel)
+                model = getattr(Maps, M)(self.mesh2)
+                assert isinstance(model, Maps.BaseModel)
             except Exception, e:
                 continue
             self.assertTrue(model.test())
 
-    def test_Mesh2MeshModel(self):
-        model = Model.Mesh2Mesh([self.mesh22, self.mesh2])
+    def test_Mesh2MeshMap(self):
+        model = Maps.Mesh2Mesh([self.mesh22, self.mesh2])
         self.assertTrue(model.test())
 
-    def test_comboModels(self):
-        combos = [(Model.LogModel, Model.Vertical1DModel)]
+    def test_comboMaps(self):
+        combos = [(Maps.ExpMap, Maps.Vertical1DMap)]
         for combo in combos:
-            model = Model.ComboModel(self.mesh2, combo)
+            model = Maps.ComboMap(self.mesh2, combo)
             self.assertTrue(model.test())
 
 
diff --git a/SimPEG/__init__.py b/SimPEG/__init__.py
index 874f4ffe..49061e09 100644
--- a/SimPEG/__init__.py
+++ b/SimPEG/__init__.py
@@ -3,7 +3,7 @@ import scipy.sparse as sp
 import Utils
 from Solver import Solver
 import Mesh
-import Model
+import Maps
 import Problem
 import Survey
 import Regularization