diff --git a/cirq-core/cirq/circuits/frozen_circuit.py b/cirq-core/cirq/circuits/frozen_circuit.py
index c1b7534ac6..08e54bdb9b 100644
--- a/cirq-core/cirq/circuits/frozen_circuit.py
+++ b/cirq-core/cirq/circuits/frozen_circuit.py
@@ -99,6 +99,7 @@ def with_tags(self, *new_tags: Hashable) -> cirq.FrozenCircuit:
             return self
         new_circuit = FrozenCircuit(tags=self.tags + new_tags)
         new_circuit._moments = self._moments
+        new_circuit.untagged = self.untagged
         return new_circuit
 
     @_compat.cached_method
diff --git a/cirq-core/cirq/circuits/frozen_circuit_test.py b/cirq-core/cirq/circuits/frozen_circuit_test.py
index 99bba012bd..5cc02d2ff2 100644
--- a/cirq-core/cirq/circuits/frozen_circuit_test.py
+++ b/cirq-core/cirq/circuits/frozen_circuit_test.py
@@ -114,6 +114,9 @@ def test_tagged_circuits() -> None:
     assert tagged_circuit.with_tags("c") == cirq.FrozenCircuit(ops, tags=[*tags, "c"])
     assert tagged_circuit.untagged == frozen_circuit
     assert frozen_circuit.untagged is frozen_circuit
+    assert frozen_circuit.with_tags(*tags).untagged is frozen_circuit
+    assert frozen_circuit.with_tags("a").untagged is frozen_circuit.with_tags("b").untagged
+    assert frozen_circuit.with_tags("a").with_tags("b").untagged is frozen_circuit
     assert tagged_circuit.unfreeze(copy=True).tags == tags
     assert tagged_circuit.unfreeze(copy=False).tags == tags
     # Test parameterized protocols