diff --git a/loopy/__init__.py b/loopy/__init__.py
index 5e36fc11159b5c0483995f6b5432f4bbb370fecf..aa2947e47dc3443dc861942def3b0bc096445a5f 100644
--- a/loopy/__init__.py
+++ b/loopy/__init__.py
@@ -358,48 +358,9 @@ def realize_cse(kernel, cse_tag, dtype, duplicate_inames=[], parallel_inames=Non
 
     # {{{ build new domain, duplicating each constraint on duplicated inames
 
-    dup_iname_dims = [kernel.iname_to_dim[iname]
-            for iname in duplicate_inames]
-    old_to_new = dict((old_iname, new_iname)
-        for old_iname, new_iname in zip(duplicate_inames, new_inames))
-
-    def realize_duplication(set):
-        start_idx = set.dim(dim_type.set)
-        result = set.insert_dims(
-                dim_type.set, start_idx,
-                len(duplicate_inames))
-
-        new_iname_to_dim = kernel.iname_to_dim.copy()
-        for i, iname in enumerate(new_inames):
-            new_idx = start_idx+i
-            result = result.set_dim_name(
-                    dim_type.set, new_idx, iname)
-            new_iname_to_dim[iname] = (dim_type.set, new_idx)
-
-
-        set_bs, = set.get_basic_sets()
-
-        for cns in set_bs.get_constraints():
-            if any(cns.involves_dims(*dim+(1,)) for dim in dup_iname_dims):
-                assert not cns.is_div_constraint()
-                if cns.is_equality():
-                    new_cns = cns.equality_alloc(result.get_space())
-                else:
-                    new_cns = cns.inequality_alloc(result.get_space())
-
-                new_coeffs = {}
-                for key, val in cns.get_coefficients_by_name().iteritems():
-                    if key in old_to_new:
-                        new_coeffs[old_to_new[key]] = val
-                    else:
-                        new_coeffs[key] = val
-
-                new_cns = new_cns.set_coefficients_by_name(new_coeffs)
-                result = result.add_constraint(new_cns)
-
-        return result, new_iname_to_dim
-
-    new_domain, new_iname_to_dim = realize_duplication(kernel.domain)
+    from loopy.isl_helpers import duplicate_axes
+    new_domain = duplicate_axes(kernel.domain, duplicate_inames, new_inames)
+    new_iname_to_dim = new_domain.get_space().get_var_dict()
 
     # }}}
 
diff --git a/loopy/isl_helpers.py b/loopy/isl_helpers.py
index de0c1f0f12fad00b678da76e7f55400b85df4144..c10082086f76d06f50f53e384162b85c954bdc7a 100644
--- a/loopy/isl_helpers.py
+++ b/loopy/isl_helpers.py
@@ -185,4 +185,46 @@ def static_value_of_pw_aff(pw_aff, constants_only):
 
 
 
+def duplicate_axes(basic_set, duplicate_inames, new_inames):
+    old_to_new = dict((old_iname, new_iname)
+        for old_iname, new_iname in zip(duplicate_inames, new_inames))
+
+    start_idx = basic_set.dim(dim_type.set)
+    result = basic_set.insert_dims(
+            dim_type.set, start_idx,
+            len(duplicate_inames))
+
+    old_var_dict = basic_set.get_space().get_var_dict()
+    dup_iname_dims = [old_var_dict[iname] for iname in duplicate_inames]
+
+    for i, iname in enumerate(new_inames):
+        new_idx = start_idx+i
+        result = result.set_dim_name(
+                dim_type.set, new_idx, iname)
+
+    set_bs, = basic_set.get_basic_sets()
+
+    for cns in set_bs.get_constraints():
+        if any(cns.involves_dims(*dim+(1,)) for dim in dup_iname_dims):
+            assert not cns.is_div_constraint()
+            if cns.is_equality():
+                new_cns = cns.equality_alloc(result.get_space())
+            else:
+                new_cns = cns.inequality_alloc(result.get_space())
+
+            new_coeffs = {}
+            for key, val in cns.get_coefficients_by_name().iteritems():
+                if key in old_to_new:
+                    new_coeffs[old_to_new[key]] = val
+                else:
+                    new_coeffs[key] = val
+
+            new_cns = new_cns.set_coefficients_by_name(new_coeffs)
+            result = result.add_constraint(new_cns)
+
+    return result
+
+
+
+
 # vim: foldmethod=marker