diff --git a/devito/finite_differences/differentiable.py b/devito/finite_differences/differentiable.py
index a20902a39a..a10c3932d8 100644
--- a/devito/finite_differences/differentiable.py
+++ b/devito/finite_differences/differentiable.py
@@ -105,7 +105,16 @@ def is_TimeDependent(self):
 
     @cached_property
     def _fd(self):
-        return dict(ChainMap(*[getattr(i, '_fd', {}) for i in self._args_diff]))
+        # Filter out all args with fd order too high
+        fd_args = []
+        for f in self._args_diff:
+            try:
+                if f.space_order <= self.space_order and \
+                        (not f.is_TimeDependent or f.time_order <= self.time_order):
+                    fd_args.append(f)
+            except AttributeError:
+                pass
+        return dict(ChainMap(*[getattr(i, '_fd', {}) for i in fd_args]))
 
     @cached_property
     def _symbolic_functions(self):
diff --git a/devito/ir/clusters/cluster.py b/devito/ir/clusters/cluster.py
index 887793e8e7..69ee00c6c5 100644
--- a/devito/ir/clusters/cluster.py
+++ b/devito/ir/clusters/cluster.py
@@ -483,7 +483,7 @@ def dtype(self):
         If two Clusters perform calculations with different precision, the
         data type with highest precision is returned.
         """
-        dtypes = {i.dtype for i in self}
+        dtypes = {i.dtype for i in self} - {None}
 
         return infer_dtype(dtypes)
 
diff --git a/tests/test_derivatives.py b/tests/test_derivatives.py
index 5fa11a6fa0..f1c1951c97 100644
--- a/tests/test_derivatives.py
+++ b/tests/test_derivatives.py
@@ -457,6 +457,21 @@ def test_all_shortcuts(self, so):
         for fd in g._fd:
             assert getattr(g, fd)
 
+        for d in grid.dimensions:
+            assert 'd%s' % d.name in f._fd
+            assert 'd%s' % d.name in g._fd
+            for o in range(2, min(7, so+1)):
+                assert 'd%s%s' % (d.name, o) in f._fd
+                assert 'd%s%s' % (d.name, o) in g._fd
+
+    def test_shortcuts_mixed(self):
+        grid = Grid(shape=(10,))
+        f = Function(name='f', grid=grid, space_order=2)
+        g = Function(name='g', grid=grid, space_order=4)
+        assert 'dx4' not in (f*g)._fd
+        assert 'dx4' not in (f+g)._fd
+        assert 'dx4' not in (g*f.dx)._fd
+
     def test_transpose_simple(self):
         grid = Grid(shape=(4, 4))
 
diff --git a/tests/test_lower_exprs.py b/tests/test_lower_exprs.py
index 4903dbf9a3..0d0b56ca82 100644
--- a/tests/test_lower_exprs.py
+++ b/tests/test_lower_exprs.py
@@ -65,9 +65,10 @@ def test_symbolic_constant_times_add(self):
         dt = grid.time_dim.spacing
 
         u = TimeFunction(name="u", grid=grid, space_order=4, time_order=2)
-        f = Function(name='f', grid=grid)
+        f = Function(name='f', grid=grid, space_order=4)
 
         eq = Eq(u.forward, u.laplace + dt**0.2*u.biharmonic(1/f))
+
         leq = collect_derivatives.func([eq])[0]
 
         assert len(eq.rhs.args) == 3