diff --git a/devito/operator/operator.py b/devito/operator/operator.py
index 609c69295f6..eb8b793f222 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 457d8476c3f..8c058170144 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 n_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 n_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 34ca370a60c..4ca4897a4dc 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.n_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,