diff --git a/devito/passes/clusters/implicit.py b/devito/passes/clusters/implicit.py
index 78454c1f1a..42e528d904 100644
--- a/devito/passes/clusters/implicit.py
+++ b/devito/passes/clusters/implicit.py
@@ -107,20 +107,25 @@ def callback(self, clusters, prefix):
             exprs, dims, sub_iterators = make_implicit_exprs(d.msd, c)
 
             # The IterationSpace induced by the MultiSubDomain
-            intervals = [Interval(i, 0, 0) for i in dims]
-            relations = (ispace0.itdimensions + dims, dims + ispace1.itdimensions)
-            ispaceN = IterationSpace(
-                IntervalGroup(intervals, relations=relations), sub_iterators
-            )
+            if dims:
+                intervals = [Interval(i) for i in dims]
+                relations = (ispace0.itdimensions + dims, dims + ispace1.itdimensions)
+                ispaceN = IterationSpace(
+                    IntervalGroup(intervals, relations=relations), sub_iterators
+                )
+                ispace = IterationSpace.union(ispace0, ispaceN)
+            else:
+                ispaceN = None
+                ispace = ispace0
 
-            ispace = IterationSpace.union(ispace0, ispaceN)
             properties = {i.dim: {SEQUENTIAL} for i in ispace}
-            if len(ispaceN) == 0:
+
+            if not ispaceN:
                 # Special case: we can factorize the thickness assignments
                 # once and for all at the top of the current IterationInterval,
                 # and reuse them for one or more (potentially non-consecutive)
                 # `clusters`
-                if ispaceN not in seen:
+                if d not in seen:
                     # Retain the guards and the syncs along the outer Dimensions
                     retained = {None} | set(c.ispace[:n-1].dimensions)
 
@@ -143,8 +148,12 @@ def callback(self, clusters, prefix):
                     )
                     tip = nxt
 
-            ispace = IterationSpace.union(c.ispace, ispaceN)
-            processed.append(c.rebuild(ispace=ispace))
+            if ispaceN:
+                ispace = IterationSpace.union(c.ispace, ispaceN)
+                processed.append(c.rebuild(ispace=ispace))
+            else:
+                processed.append(c)
+            seen.add(d)
 
         return processed
 
diff --git a/devito/types/grid.py b/devito/types/grid.py
index faecb25236..de91284441 100644
--- a/devito/types/grid.py
+++ b/devito/types/grid.py
@@ -725,7 +725,8 @@ def __subdomain_finalize__(self, grid, counter=0, **kwargs):
 
         # Create the SubDomainSet SubDimensions
         self._dimensions = tuple(
-            MultiSubDimension('%si' % d.name, d, self) for d in grid.dimensions
+            MultiSubDimension('%si%d' % (d.name, counter), d, self)
+            for d in grid.dimensions
         )
 
         # Compute the SubDomainSet shapes
diff --git a/tests/test_subdomains.py b/tests/test_subdomains.py
index f7a8c3df4d..984f2c29ef 100644
--- a/tests/test_subdomains.py
+++ b/tests/test_subdomains.py
@@ -447,7 +447,7 @@ class DummySubdomains(SubDomainSet):
         # Make sure it jit-compiles
         op.cfunction
 
-        assert_structure(op, ['x,y', 't,n0', 't,n0,xi,yi'], 'x,y,t,n0,xi,yi')
+        assert_structure(op, ['x,y', 't,n0', 't,n0,xi2,yi2'], 'x,y,t,n0,xi2,yi2')
 
     def test_issue_1761_b(self):
         """
@@ -486,8 +486,8 @@ class DummySubdomains2(SubDomainSet):
         op.cfunction
 
         assert_structure(op,
-                         ['x,y', 't,n0', 't,n0,xi,yi', 't,n1', 't,n1,xi,yi'],
-                         'x,y,t,n0,xi,yi,n1,xi,yi')
+                         ['x,y', 't,n0', 't,n0,xi2,yi2', 't,n1', 't,n1,xi3,yi3'],
+                         'x,y,t,n0,xi2,yi2,n1,xi3,yi3')
 
     def test_issue_1761_c(self):
         """
@@ -522,9 +522,9 @@ class DummySubdomains2(SubDomainSet):
         # Make sure it jit-compiles
         op.cfunction
 
-        assert_structure(op, ['x,y', 't,n0', 't,n0,xi,yi',
-                              't,n1', 't,n1,xi,yi', 't,n0', 't,n0,xi,yi'],
-                         'x,y,t,n0,xi,yi,n1,xi,yi,n0,xi,yi')
+        assert_structure(op, ['x,y', 't,n0', 't,n0,xi2,yi2',
+                              't,n1', 't,n1,xi3,yi3', 't,n0', 't,n0,xi2,yi2'],
+                         'x,y,t,n0,xi2,yi2,n1,xi3,yi3,n0,xi2,yi2')
 
     def test_issue_1761_d(self):
         """
@@ -549,7 +549,8 @@ class Dummy(SubDomainSet):
         # Make sure it jit-compiles
         op.cfunction
 
-        assert_structure(op, ['t,n0', 't,n0,xi,yi', 't,n0,xi,yi'], 't,n0,xi,yi,xi,yi')
+        assert_structure(op, ['t,n0', 't,n0,xi2,yi2', 't,n0,xi2,yi2'],
+                         't,n0,xi2,yi2,xi2,yi2')
 
     def test_guarding(self):
 
@@ -576,8 +577,8 @@ class Dummy(SubDomainSet):
         # Make sure it jit-compiles
         op.cfunction
 
-        assert_structure(op, ['t', 't,n0', 't,n0,xi,yi', 't,n0', 't,n0,xi,yi'],
-                         't,n0,xi,yi,n0,xi,yi')
+        assert_structure(op, ['t', 't,n0', 't,n0,xi2,yi2', 't,n0', 't,n0,xi2,yi2'],
+                         't,n0,xi2,yi2,n0,xi2,yi2')
 
     def test_3D(self):
 
@@ -597,8 +598,8 @@ class Dummy(SubDomainSet):
         # Make sure it jit-compiles
         op.cfunction
 
-        assert_structure(op, ['t,n0', 't,n0,xi0_blk0,yi0_blk0,xi,yi,zi'],
-                         't,n0,xi0_blk0,yi0_blk0,xi,yi,zi')
+        assert_structure(op, ['t,n0', 't,n0,xi20_blk0,yi20_blk0,xi2,yi2,zi2'],
+                         't,n0,xi20_blk0,yi20_blk0,xi2,yi2,zi2')
 
     def test_sequential_implicit(self):
         """