diff --git a/devito/ir/stree/algorithms.py b/devito/ir/stree/algorithms.py
index d8bbb4958a..0f7e46bcfd 100644
--- a/devito/ir/stree/algorithms.py
+++ b/devito/ir/stree/algorithms.py
@@ -147,10 +147,10 @@ def preprocess(clusters, options=None, **kwargs):
             found = []
             for c1 in list(queue):
                 distributed_aindices = c1.halo_scheme.distributed_aindices
-                h_indices = set().union(*[(d, d.root)
-                                          for d in c1.halo_scheme.loc_indices])
+                h_indices = set().union(*[d._defines for d in c1.halo_scheme.loc_indices])
 
-                # Skip if the Halo echange would end up outside its need iteration space
+                # Skip if the halo exchange would end up outside
+                # its iteration space
                 if h_indices and not h_indices & dims:
                     continue
 
diff --git a/devito/operator/operator.py b/devito/operator/operator.py
index 609c69295f..eb8b793f22 100644
--- a/devito/operator/operator.py
+++ b/devito/operator/operator.py
@@ -578,6 +578,7 @@ def _prepare_arguments(self, autotune=None, **kwargs):
         if len(discretizations) > 1:
             discretizations = {g for g in discretizations
                                if not any(d.is_Derived for d in g.dimensions)}
+
         for i in discretizations:
             args.update(i._arg_values(**kwargs))
 
@@ -590,9 +591,6 @@ def _prepare_arguments(self, autotune=None, **kwargs):
             if configuration['mpi']:
                 raise ValueError("Multiple Grids found")
         try:
-            # Take biggest grid, i.e discard grids with subdimensions
-            grids = {g for g in grids if not any(d.is_Sub for d in g.dimensions)}
-            # First grid as there is no heuristic on how to choose from the leftovers
             grid = grids.pop()
         except KeyError:
             grid = None
diff --git a/devito/passes/iet/langbase.py b/devito/passes/iet/langbase.py
index 457d8476c3..2acccba648 100644
--- a/devito/passes/iet/langbase.py
+++ b/devito/passes/iet/langbase.py
@@ -214,8 +214,8 @@ def DeviceIteration(self):
     def Prodder(self):
         return self.lang.Prodder
 
-    def _n_device_pointers(self, *args, **kwargs):
-        return 0
+    def _device_pointers(self, *args, **kwargs):
+        return {}
 
 
 class DeviceAwareMixin(object):
@@ -328,11 +328,10 @@ def _(iet):
 
         return _initialize(iet)
 
-    def _n_device_pointers(self, iet):
+    def _device_pointers(self, iet):
         functions = FindSymbols().visit(iet)
         devfuncs = [f for f in functions if f.is_Array and f._mem_local]
-
-        return len(devfuncs)
+        return set(devfuncs)
 
     def _is_offloadable(self, iet):
         """
@@ -345,8 +344,7 @@ def _is_offloadable(self, iet):
         functions = FindSymbols().visit(iet)
         buffers = [f for f in functions if f.is_Array and f._mem_mapped]
         hostfuncs = [f for f in functions if not is_on_device(f, self.gpu_fit)]
-
-        return not (hostfuncs and buffers)
+        return not (buffers and hostfuncs)
 
 
 class Sections(tuple):
diff --git a/devito/passes/iet/parpragma.py b/devito/passes/iet/parpragma.py
index 34ca370a60..b6476192b2 100644
--- a/devito/passes/iet/parpragma.py
+++ b/devito/passes/iet/parpragma.py
@@ -301,7 +301,7 @@ def _select_candidates(self, candidates):
             # Iterations and their position (i.e. outermost to innermost) in the nest
             score = (
                 int(root.is_ParallelNoAtomic),
-                self._n_device_pointers(root),  # Outermost offloadable
+                len(self._device_pointers(root)),  # Outermost offloadable
                 int(len([i for i in collapsable if i.is_ParallelNoAtomic]) >= 1),
                 int(len([i for i in collapsable if i.is_ParallelRelaxed]) >= 1),
                 -(n0 + 1)  # The outermost, the better
@@ -375,7 +375,7 @@ def _make_partree(self, candidates, nthreads=None):
                                           ncollapsed=ncollapsed, nthreads=nthreads,
                                           **root.args)
             prefix = []
-        elif all(i.is_ParallelRelaxed for i in candidates) and nthreads is not None:
+        elif nthreads is not None:
             body = self.HostIteration(schedule='static',
                                       parallel=nthreads is not self.nthreads_nested,
                                       ncollapsed=ncollapsed, nthreads=nthreads,
@@ -383,7 +383,6 @@ def _make_partree(self, candidates, nthreads=None):
             prefix = []
         else:
             # pragma ... for ... schedule(..., expr)
-            assert nthreads is None
             nthreads = self.nthreads_nonaffine
             chunk_size = Symbol(name='chunk_size')
             body = self.HostIteration(ncollapsed=ncollapsed, chunk_size=chunk_size,
diff --git a/devito/types/dimension.py b/devito/types/dimension.py
index 2d11ccb220..43865c72f5 100644
--- a/devito/types/dimension.py
+++ b/devito/types/dimension.py
@@ -983,7 +983,7 @@ def symbolic_incr(self):
     def bound_symbols(self):
         return set(self.parent.bound_symbols)
 
-    def _arg_defaults(self, alias=None, **kwargs):
+    def _arg_defaults(self, **kwargs):
         return {}
 
     def _arg_values(self, *args, **kwargs):
@@ -1452,7 +1452,7 @@ def symbolic_max(self):
     def _arg_names(self):
         return (self.min_name, self.max_name, self.name) + self.parent._arg_names
 
-    def _arg_defaults(self, _min=None, size=None, **kwargs):
+    def _arg_defaults(self, _min=None, **kwargs):
         """
         A map of default argument values defined by this dimension.