diff --git a/devito/passes/iet/misc.py b/devito/passes/iet/misc.py
index 4617b47336..56cbe73f52 100644
--- a/devito/passes/iet/misc.py
+++ b/devito/passes/iet/misc.py
@@ -5,9 +5,10 @@
 import sympy
 
 from devito.finite_differences import Max, Min
-from devito.ir import (Any, Forward, List, Prodder, FindApplications, FindNodes,
-                       FindSymbols, Transformer, Uxreplace, filter_iterations,
-                       retrieve_iteration_tree, pull_dims)
+from devito.ir import (Any, Forward, DummyExpr, Iteration, List, Prodder,
+                       FindApplications, FindNodes, FindSymbols, Transformer,
+                       Uxreplace, filter_iterations, retrieve_iteration_tree,
+                       pull_dims)
 from devito.passes.iet.engine import iet_pass
 from devito.ir.iet.efunc import DeviceFunction, EntryFunction
 from devito.symbolics import (ValueLimit, evalrel, has_integer_args, limits_mapper,
@@ -231,10 +232,13 @@ def minimize_symbols(iet):
 
         * Remove redundant ModuloDimensions (e.g., due to using the
           `save=Buffer(2)` API)
+        * Simplify Iteration headers (e.g., ModuloDimensions with identical
+          starting point and step)
         * Abridge SubDimension names where possible to declutter generated
           loop nests and shrink indices
     """
     iet = remove_redundant_moddims(iet)
+    iet = simplify_iteration_headers(iet)
     iet = abridge_dim_names(iet)
 
     return iet, {}
@@ -264,6 +268,29 @@ def remove_redundant_moddims(iet):
     return iet
 
 
+def simplify_iteration_headers(iet):
+    mapper = {}
+    for i in FindNodes(Iteration).visit(iet):
+        candidates = [d for d in i.uindices
+                      if d.is_Modulo and d.symbolic_min == d.symbolic_incr]
+
+        # Don't touch `t0, t1, ...` for codegen aesthetics and to avoid
+        # massive changes in the test suite
+        candidates = [d for d in candidates if not d.is_Time]
+
+        if not candidates:
+            continue
+
+        uindices = [d for d in i.uindices if d not in candidates]
+        stmts = [DummyExpr(d, d.symbolic_incr, init=True) for d in candidates]
+
+        mapper[i] = i._rebuild(nodes=tuple(stmts) + i.nodes, uindices=uindices)
+
+    iet = Transformer(mapper, nested=True).visit(iet)
+
+    return iet
+
+
 @singledispatch
 def abridge_dim_names(iet):
     return iet
diff --git a/tests/test_dse.py b/tests/test_dse.py
index 7fd0298d93..e0450bc61d 100644
--- a/tests/test_dse.py
+++ b/tests/test_dse.py
@@ -1131,13 +1131,13 @@ def test_from_different_nests(self, rotate):
         # Check code generation
         bns, _ = assert_blocking(op1, {'x0_blk0', 'x1_blk0'})
         trees = retrieve_iteration_tree(bns['x0_blk0'])
-        assert len(trees) == 2
-        assert trees[0][-1].nodes[0].body[0].write.is_Array
-        assert trees[1][-1].nodes[0].body[0].write is u
+        assert len(trees) == 4 if rotate else 2
+        assert trees[-2][-1].nodes[0].body[0].write.is_Array
+        assert trees[-1][-1].nodes[0].body[0].write is u
         trees = retrieve_iteration_tree(bns['x1_blk0'])
-        assert len(trees) == 2
-        assert trees[0][-1].nodes[0].body[0].write.is_Array
-        assert trees[1][-1].nodes[0].body[0].write is v
+        assert len(trees) == 4 if rotate else 2
+        assert trees[-2][-1].nodes[0].body[0].write.is_Array
+        assert trees[-1][-1].nodes[0].body[0].write is v
 
         # Check numerical output
         op0(time_M=1)