diff --git a/devito/ir/iet/nodes.py b/devito/ir/iet/nodes.py
index 378d0be721..72ff6e3c04 100644
--- a/devito/ir/iet/nodes.py
+++ b/devito/ir/iet/nodes.py
@@ -16,7 +16,7 @@
                                Forward, WithLock, PrefetchUpdate, detect_io)
 from devito.symbolics import ListInitializer, CallFromPointer, ccode
 from devito.tools import (Signer, as_tuple, filter_ordered, filter_sorted, flatten,
-                          ctypes_to_cstr)
+                          ctypes_to_cstr, OrderedSet)
 from devito.types.basic import (AbstractFunction, AbstractSymbol, Basic, Indexed,
                                 Symbol)
 from devito.types.object import AbstractObject, LocalObject
@@ -1459,7 +1459,7 @@ def __init__(self, body, halo_scheme):
     def __repr__(self):
         fstrings = []
         for f in self.functions:
-            loc_indices = set().union(*[self.halo_scheme.fmapper[f].loc_indices.values()])
+            loc_indices = OrderedSet(*(self.halo_scheme.fmapper[f].loc_indices.values()))
             loc_indices_str = str(list(loc_indices)) if loc_indices else ""
 
             fstrings.append(f"{f.name}{loc_indices_str}")
diff --git a/devito/mpi/halo_scheme.py b/devito/mpi/halo_scheme.py
index cc9edbe416..64a47623ff 100644
--- a/devito/mpi/halo_scheme.py
+++ b/devito/mpi/halo_scheme.py
@@ -11,7 +11,7 @@
 from devito.ir.support import Forward, Scope
 from devito.symbolics.manipulation import _uxreplace_registry
 from devito.tools import (Reconstructable, Tag, as_tuple, filter_ordered, flatten,
-                          frozendict, is_integer, filter_sorted)
+                          frozendict, is_integer, filter_sorted, OrderedSet)
 from devito.types import Grid
 
 __all__ = ['HaloScheme', 'HaloSchemeEntry', 'HaloSchemeException', 'HaloTouch']
@@ -28,7 +28,9 @@ class HaloLabel(Tag):
 STENCIL = HaloLabel('stencil')
 
 
-class HaloSchemeEntry:
+class HaloSchemeEntry(Reconstructable):
+
+    __rkwargs__ = ('loc_indices', 'loc_dirs', 'halos', 'dims')
 
     def __init__(self, loc_indices, loc_dirs, halos, dims):
         self.loc_indices = loc_indices
@@ -36,10 +38,6 @@ def __init__(self, loc_indices, loc_dirs, halos, dims):
         self.halos = halos
         self.dims = dims
 
-    def __repr__(self):
-        return (f"HaloSchemeEntry(loc_indices={self.loc_indices}, "
-                f"loc_dirs={self.loc_dirs}, halos={self.halos}, dims={self.dims})")
-
     def __eq__(self, other):
         if not isinstance(other, HaloSchemeEntry):
             return False
@@ -54,12 +52,9 @@ def __hash__(self):
                      frozenset(self.halos),
                      frozenset(self.dims)))
 
-    def rebuild(self, **kwargs):
-        loc_indices = kwargs.get('loc_indices', self.loc_indices)
-        loc_dirs = kwargs.get('loc_dirs', self.loc_dirs)
-        halos = kwargs.get('halos', self.halos)
-        dims = kwargs.get('dims', self.dims)
-        return HaloSchemeEntry(loc_indices, loc_dirs, halos, dims)
+    def __repr__(self):
+        return (f"HaloSchemeEntry(loc_indices={self.loc_indices}, "
+                f"loc_dirs={self.loc_dirs}, halos={self.halos}, dims={self.dims})")
 
 
 Halo = namedtuple('Halo', 'dim side')
@@ -129,7 +124,7 @@ def __init__(self, exprs, ispace):
     def __repr__(self):
         fstrings = []
         for f in self.fmapper:
-            loc_indices = set().union(*[self._mapper[f].loc_indices.values()])
+            loc_indices = OrderedSet(*(self._mapper[f].loc_indices.values()))
             loc_indices_str = str(list(loc_indices)) if loc_indices else ""
 
             fstrings.append(f"{f.name}{loc_indices_str}")
diff --git a/devito/passes/iet/mpi.py b/devito/passes/iet/mpi.py
index 323b390c7f..72e351bc84 100644
--- a/devito/passes/iet/mpi.py
+++ b/devito/passes/iet/mpi.py
@@ -109,7 +109,6 @@ def _hoist_halospots(iet):
                         continue
 
                     for it in iters:
-                        # If also merge-able we can start hoisting the latter
                         for dep in scopes[it].d_flow.project(f):
                             if not any(r(dep, hs1, v.loc_indices) for r in merge_rules()):
                                 break
@@ -120,17 +119,18 @@ def _hoist_halospots(iet):
                             # the loc_indices with known values
                             # TODO: Can I get this in a more elegant way?
                             for d in hse.loc_indices:
-                                if hse.loc_indices[d].is_Symbol:
-                                    assert d in hse.loc_indices[d]._defines
-                                    root_min = hse.loc_indices[d].symbolic_min
-                                    new_min = root_min.subs(hse.loc_indices[d].root,
-                                                            hse.loc_indices[d].root.symbolic_min)
+                                md = hse.loc_indices[d]
+                                if md.is_Symbol:
+                                    root = md.root
+                                    hse_min = md.symbolic_min
+                                    new_min = hse_min.subs(root, root.symbolic_min)
                                     raw_loc_indices[d] = new_min
                                 else:
-                                    assert d.symbolic_min in hse.loc_indices[d].free_symbols
-                                    raw_loc_indices[d] = hse.loc_indices[d]
+                                    # md is in form of an expression
+                                    assert d.symbolic_min in md.free_symbols
+                                    raw_loc_indices[d] = md
 
-                            hse = hse.rebuild(loc_indices=frozendict(raw_loc_indices))
+                            hse = hse._rebuild(loc_indices=frozendict(raw_loc_indices))
                             hs1.halo_scheme.fmapper[f] = hse
 
                             hsmapper[hs1] = hsmapper.get(hs1, hs1.halo_scheme).drop(f)