diff --git a/devito/finite_differences/differentiable.py b/devito/finite_differences/differentiable.py
index 23152053b84..a10c3932d80 100644
--- a/devito/finite_differences/differentiable.py
+++ b/devito/finite_differences/differentiable.py
@@ -109,7 +109,8 @@ def _fd(self):
         fd_args = []
         for f in self._args_diff:
             try:
-                if f.space_order <= self.space_order and f.time_order <= self.time_order:
+                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
diff --git a/devito/ir/clusters/cluster.py b/devito/ir/clusters/cluster.py
index 887793e8e7e..69ee00c6c5b 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)