diff --git a/devito/__init__.py b/devito/__init__.py
index ef08d206f2..c03324a39c 100644
--- a/devito/__init__.py
+++ b/devito/__init__.py
@@ -75,7 +75,7 @@ def reinit_compiler(val):
                   deprecate='openmp')
 
 # MPI mode (0 => disabled, 1 == basic)
-preprocessor = lambda i: bool(i) if isinstance(i, int) else i
+preprocessor = lambda i: {0: False, 1: 'basic'}.get(i, i)
 configuration.add('mpi', 0, [0, 1] + list(mpi_registry),
                   preprocessor=preprocessor, callback=reinit_compiler)
 
diff --git a/devito/ir/clusters/algorithms.py b/devito/ir/clusters/algorithms.py
index b463593438..1a05f0842a 100644
--- a/devito/ir/clusters/algorithms.py
+++ b/devito/ir/clusters/algorithms.py
@@ -358,12 +358,8 @@ def rule(size, e):
             groups = as_mapper(mds, lambda d: d.modulo)
             for size, v in groups.items():
                 key = partial(rule, size)
-                if size == 1:
-                    # Optimization -- avoid useless "% 1" ModuloDimensions
-                    subs = {md.origin: 0 for md in v}
-                else:
-                    subs = {md.origin: md for md in v}
-                    sub_iterators[d].extend(v)
+                subs = {md.origin: md for md in v}
+                sub_iterators[d].extend(v)
 
                 func = partial(xreplace_indices, mapper=subs, key=key)
                 exprs = [e.apply(func) for e in exprs]
diff --git a/devito/mpi/routines.py b/devito/mpi/routines.py
index dc89e85164..8b4987c8bb 100644
--- a/devito/mpi/routines.py
+++ b/devito/mpi/routines.py
@@ -1002,7 +1002,6 @@ def _call_poke(self, poke):
 
 
 mpi_registry = {
-    True: BasicHaloExchangeBuilder,
     'basic': BasicHaloExchangeBuilder,
     'diag': DiagHaloExchangeBuilder,
     'diag2': Diag2HaloExchangeBuilder,
diff --git a/devito/passes/iet/misc.py b/devito/passes/iet/misc.py
index f0b2b7f4f5..0b4ed39149 100644
--- a/devito/passes/iet/misc.py
+++ b/devito/passes/iet/misc.py
@@ -246,25 +246,31 @@ def remove_redundant_moddims(iet):
     if not mds:
         return iet
 
-    mapper = as_mapper(mds, key=lambda md: md.offset % md.modulo)
+    # ModuloDimensions are defined in Iteration headers, hence they must be
+    # removed from there first of all
+    mapper = {}
+    for n in FindNodes(Iteration).visit(iet):
+        candidates = [d for d in n.uindices if d in mds]
 
-    subs = {}
-    for k, v in mapper.items():
-        chosen = v.pop(0)
-        subs.update({d: chosen for d in v})
+        degenerates, others = split(candidates, lambda d: d.modulo == 1)
+        subs = {d: sympy.S.Zero for d in degenerates}
 
-    body = Uxreplace(subs).visit(iet.body)
-    iet = iet._rebuild(body=body)
+        redundants = as_mapper(others, key=lambda d: d.offset % d.modulo)
+        for k, v in redundants.items():
+            chosen = v.pop(0)
+            subs.update({d: chosen for d in v})
 
-    # ModuloDimensions are defined in Iteration headers, hence they must be
-    # removed from there too
-    subs = {}
-    for n in FindNodes(Iteration).visit(iet):
-        if not set(n.uindices) & set(mds):
-            continue
-        subs[n] = n._rebuild(uindices=filter_ordered(n.uindices))
+        if subs:
+            # Expunge the ModuloDimensions from the Iteration header
+            uindices = [d for d in n.uindices if d not in subs]
+            iteration = n._rebuild(uindices=uindices)
 
-    iet = Transformer(subs, nested=True).visit(iet)
+            # Replace the ModuloDimensions in the Iteration body
+            iteration = Uxreplace(subs).visit(iteration)
+
+            mapper[n] = iteration
+
+    iet = Transformer(mapper, nested=True).visit(iet)
 
     return iet
 
diff --git a/tests/test_gpu_common.py b/tests/test_gpu_common.py
index 3980b60cd2..70879b4ce7 100644
--- a/tests/test_gpu_common.py
+++ b/tests/test_gpu_common.py
@@ -161,7 +161,7 @@ def test_reduction_many_dims(self):
         op1 = Operator(eqns, opt=('advanced', {'mapify-reduce': True}))
 
         tree, = retrieve_iteration_tree(op0)
-        assert 'collapse(4) reduction(+:s)' in str(tree.root.pragmas[0])
+        assert 'collapse(3) reduction(+:s)' in str(tree[1].pragmas[0])
 
         tree, = retrieve_iteration_tree(op1)
         assert 'collapse(3) reduction(+:s)' in str(tree[1].pragmas[0])
diff --git a/tests/test_mpi.py b/tests/test_mpi.py
index c8bad20aaa..b6332a476c 100644
--- a/tests/test_mpi.py
+++ b/tests/test_mpi.py
@@ -4,10 +4,10 @@
 
 from conftest import _R, assert_blocking, assert_structure
 from devito import (Grid, Constant, Function, TimeFunction, SparseFunction,
-                    SparseTimeFunction, Dimension, ConditionalDimension,
+                    SparseTimeFunction, Dimension, ConditionalDimension, div,
                     SubDimension, SubDomain, Eq, Ne, Inc, NODE, Operator, norm,
                     inner, configuration, switchconfig, generic_derivative,
-                    PrecomputedSparseFunction, DefaultDimension)
+                    PrecomputedSparseFunction, DefaultDimension, Buffer)
 from devito.arch.compiler import OneapiCompiler
 from devito.data import LEFT, RIGHT
 from devito.ir.iet import (Call, Conditional, Iteration, FindNodes, FindSymbols,
@@ -1639,6 +1639,28 @@ def test_enforce_haloupdate_if_unwritten_function(self, mode):
         calls = FindNodes(Call).visit(op)
         assert len(calls) == 2   # One for `v` and one for `usave`
 
+    @pytest.mark.parallel(mode=1)
+    def test_haloupdate_buffer1(self, mode):
+        grid = Grid(shape=(4, 4))
+        x, y = grid.dimensions
+
+        u = TimeFunction(name='u', grid=grid, time_order=1, save=Buffer(1))
+        v = TimeFunction(name='v', grid=grid, time_order=1, save=Buffer(1))
+
+        eqns = [Eq(u.forward, div(v) + 1.),
+                Eq(v.forward, div(u.forward) + 1.)]
+
+        op = Operator(eqns)
+
+        calls = FindNodes(Call).visit(op)
+        # There should be two separate calls
+        # halo(v), eq_u, halo_u, eq(v)
+        assert len(calls) == 2
+
+        # Also ensure the compiler is doing its job removing unnecessary
+        # ModuloDimensions
+        assert len([i for i in FindSymbols('dimensions').visit(op) if i.is_Modulo]) == 0
+
 
 class TestOperatorAdvanced: