diff --git a/cirq-core/cirq/transformers/transformer_primitives.py b/cirq-core/cirq/transformers/transformer_primitives.py
index 9eb3add785e..a5035ec7f62 100644
--- a/cirq-core/cirq/transformers/transformer_primitives.py
+++ b/cirq-core/cirq/transformers/transformer_primitives.py
@@ -23,6 +23,7 @@
     List,
     Optional,
     Sequence,
+    Union,
     TYPE_CHECKING,
 )
 
@@ -57,7 +58,7 @@ def _create_target_circuit_type(ops: ops.OP_TREE, target_circuit: CIRCUIT_TYPE)
 
 def map_moments(
     circuit: CIRCUIT_TYPE,
-    map_func: Callable[[ops.Moment, int], Sequence[ops.Moment]],
+    map_func: Callable[[ops.Moment, int], Union[ops.Moment, Sequence[ops.Moment]]],
 ) -> CIRCUIT_TYPE:
     """Applies local transformation on moments, by calling `map_func(moment)` for each moment.
 
@@ -76,6 +77,8 @@ def map_moments(
 def map_operations(
     circuit: CIRCUIT_TYPE,
     map_func: Callable[[ops.Operation, int], ops.OP_TREE],
+    *,
+    raise_if_add_qubits=True,
 ) -> CIRCUIT_TYPE:
     """Applies local transformations on operations, by calling `map_func(op)` for each op.
 
@@ -88,9 +91,12 @@ def map_operations(
             `cirq.CircuitOperation(cirq.FrozenCircuit(op_tree)).with_tags(MAPPED_CIRCUIT_OP_TAG)`
             to preserve moment structure. Utility methods like `cirq.unroll_circuit_op` can
             subsequently be used to unroll the mapped circuit operation.
+        raise_if_add_qubits: Set to True by default. If True, Raises ValueError if `map_func(op)`
+            adds operations on qubits outside of `op.qubits`.
 
     Raises:
-          ValueError if `issubset(qubit_set(map_func(op)), op.qubits) is False`.
+          ValueError if `issubset(qubit_set(map_func(op)), op.qubits) is False` and
+            `raise_if_add_qubits is True`.
 
     Returns:
         Copy of input circuit with mapped operations (wrapped in a tagged CircuitOperation).
@@ -98,14 +104,15 @@ def map_operations(
 
     def apply_map(op: ops.Operation, idx: int) -> ops.OP_TREE:
         c = circuits.FrozenCircuit(map_func(op, idx))
-        if not c.all_qubits().issubset(op.qubits):
+        if raise_if_add_qubits and not c.all_qubits().issubset(op.qubits):
             raise ValueError(
                 f"Mapped operations {c.all_operations()} should act on a subset "
                 f"of qubits of the original operation {op}"
             )
-        if len(c) == 1:
-            # All operations act in the same moment; so we don't need to wrap them in a circuit_op.
-            return c[0].operations
+        if len(c) <= 1:
+            # Either empty circuit or all operations act in the same moment;
+            # So, we don't need to wrap them in a circuit_op.
+            return c[0].operations if c else []
         circuit_op = circuits.CircuitOperation(c).with_tags(MAPPED_CIRCUIT_OP_TAG)
         return circuit_op
 
diff --git a/cirq-core/cirq/transformers/transformer_primitives_test.py b/cirq-core/cirq/transformers/transformer_primitives_test.py
index 7911fc5de35..b851f537d7a 100644
--- a/cirq-core/cirq/transformers/transformer_primitives_test.py
+++ b/cirq-core/cirq/transformers/transformer_primitives_test.py
@@ -195,6 +195,21 @@ def test_map_operations_raises_qubits_not_subset():
         )
 
 
+def test_map_operations_can_add_qubits_if_flag_false():
+    q = cirq.LineQubit.range(2)
+    c = cirq.Circuit(cirq.H(q[0]))
+    c_mapped = cirq.map_operations(c, lambda *_: cirq.CNOT(q[0], q[1]), raise_if_add_qubits=False)
+    cirq.testing.assert_same_circuits(c_mapped, cirq.Circuit(cirq.CNOT(q[0], q[1])))
+
+
+def test_map_operations_can_drop_operations():
+    q = cirq.LineQubit.range(2)
+    c = cirq.Circuit(cirq.X(q[0]), cirq.Y(q[1]), cirq.X(q[1]), cirq.Y(q[0]))
+    c_mapped = cirq.map_operations(c, lambda op, _: op if op.gate == cirq.X else [])
+    c_expected = cirq.Circuit(cirq.Moment(cirq.X(q[0])), cirq.Moment(cirq.X(q[1])))
+    cirq.testing.assert_same_circuits(c_mapped, c_expected)
+
+
 def test_map_moments_drop_empty_moments():
     op = cirq.X(cirq.NamedQubit("x"))
     c = cirq.Circuit(cirq.Moment(op), cirq.Moment(), cirq.Moment(op))