diff --git a/mathics/core/symbols.py b/mathics/core/symbols.py
index 75c7f1b51..cb434f855 100644
--- a/mathics/core/symbols.py
+++ b/mathics/core/symbols.py
@@ -465,9 +465,14 @@ def evaluate(self, evaluation):
                     from mathics.core.systemsymbols import SymbolAborted
 
                     return SymbolAborted
+                # iteration_count is the length of the current chain of
+                # rewrites (x -> y -> ...), not a total for the whole
+                # evaluation: each finished lookup gives its step back.
                 evaluation.iteration_count += 1
-
-                return result.evaluate(evaluation)
+                try:
+                    return result.evaluate(evaluation)
+                finally:
+                    evaluation.iteration_count -= 1
         return self
 
     def get_head(self) -> "Symbol":
diff --git a/test/builtin/test_evaluation.py b/test/builtin/test_evaluation.py
index 1d635991d..e0a8c4169 100644
--- a/test/builtin/test_evaluation.py
+++ b/test/builtin/test_evaluation.py
@@ -3,7 +3,6 @@
 Unit tests from mathics.builtin.evaluation.
 """
 
-
 import sys
 from test.helper import check_evaluation_as_in_cli
 
@@ -55,6 +54,32 @@
             None,
         ),
         ("ClearAll[f];", None, None, None),
+        # $IterationLimit bounds one chain of rewrites, not the number of
+        # times symbols are looked up during the whole evaluation.
+        (
+            "Block[{$IterationLimit = 20, itlimX = {itlimA}}, Do[itlimX, {30}]; itlimX]",
+            None,
+            "{itlimA}",
+            "Many separate lookups of a symbol do not add up",
+        ),
+        (
+            'Do[Evaluate[Symbol["c" <> ToString[k]]] = Symbol["c" <> ToString[k + 1]], {k, 0, 29}]; Block[{$IterationLimit = 40}, c0]',
+            None,
+            "c30",
+            "A chain of 30 rewrites is within the limit of 40",
+        ),
+        (
+            "Block[{$IterationLimit = 20}, c0]",
+            ("Iteration limit of 20 exceeded.",),
+            "$Aborted",
+            "A chain of 30 rewrites exceeds the limit of 20",
+        ),
+        (
+            'ClearAll[c0, c30]; Do[ClearAll[Evaluate[Symbol["c" <> ToString[k]]]], {k, 1, 29}];',
+            None,
+            None,
+            None,
+        ),
         (
             "Attributes[h] = Flat;h[items___] := Plus[items];h[1, Unevaluated[Sequence[Unevaluated[2], 3]], Sequence[4, Unevaluated[5]]]",
             None,