diff --git a/cirq-core/cirq/circuits/frozen_circuit_test.py b/cirq-core/cirq/circuits/frozen_circuit_test.py
index 8e89332af04..01b211cad32 100644
--- a/cirq-core/cirq/circuits/frozen_circuit_test.py
+++ b/cirq-core/cirq/circuits/frozen_circuit_test.py
@@ -68,5 +68,9 @@ def test_immutable():
     q = cirq.LineQubit(0)
     c = cirq.FrozenCircuit(cirq.X(q), cirq.H(q))
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    # Match one of two strings. The second one is message returned since python 3.11.
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'moments' of 'FrozenCircuit' object has no setter)",
+    ):
         c.moments = (cirq.Moment(cirq.H(q)), cirq.Moment(cirq.X(q)))
diff --git a/cirq-core/cirq/devices/grid_qubit_test.py b/cirq-core/cirq/devices/grid_qubit_test.py
index 6b4b3045b38..cce810c3930 100644
--- a/cirq-core/cirq/devices/grid_qubit_test.py
+++ b/cirq-core/cirq/devices/grid_qubit_test.py
@@ -335,23 +335,39 @@ def test_to_json():
 
 
 def test_immutable():
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    # Match one of two strings. The second one is message returned since python 3.11.
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'col' of 'GridQubit' object has no setter)",
+    ):
         q = cirq.GridQubit(1, 2)
         q.col = 3
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'row' of 'GridQubit' object has no setter)",
+    ):
         q = cirq.GridQubit(1, 2)
         q.row = 3
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'col' of 'GridQid' object has no setter)",
+    ):
         q = cirq.GridQid(1, 2, dimension=3)
         q.col = 3
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'row' of 'GridQid' object has no setter)",
+    ):
         q = cirq.GridQid(1, 2, dimension=3)
         q.row = 3
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'dimension' of 'GridQid' object has no setter)",
+    ):
         q = cirq.GridQid(1, 2, dimension=3)
         q.dimension = 3
 
diff --git a/cirq-core/cirq/devices/line_qubit_test.py b/cirq-core/cirq/devices/line_qubit_test.py
index cb91ef06086..6c8474f313a 100644
--- a/cirq-core/cirq/devices/line_qubit_test.py
+++ b/cirq-core/cirq/devices/line_qubit_test.py
@@ -242,11 +242,18 @@ def _qid_shape_(self):
 
 
 def test_immutable():
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    # Match one of two strings. The second one is message returned since python 3.11.
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'x' of 'LineQubit' object has no setter)",
+    ):
         q = cirq.LineQubit(5)
         q.x = 6
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'x' of 'LineQid' object has no setter)",
+    ):
         q = cirq.LineQid(5, dimension=4)
         q.x = 6
 
diff --git a/cirq-core/cirq/ops/gate_operation_test.py b/cirq-core/cirq/ops/gate_operation_test.py
index e37d62df183..bce07dce0e9 100644
--- a/cirq-core/cirq/ops/gate_operation_test.py
+++ b/cirq-core/cirq/ops/gate_operation_test.py
@@ -41,10 +41,19 @@ def test_immutable():
     a, b = cirq.LineQubit.range(2)
     op = cirq.X(a)
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    # Match one of two strings. The second one is message returned since python 3.11.
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|"
+        "(property 'gate' of 'SingleQubitPauliStringGateOperation' object has no setter)",
+    ):
         op.gate = cirq.Y
 
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|"
+        "(property 'qubits' of 'SingleQubitPauliStringGateOperation' object has no setter)",
+    ):
         op.qubits = [b]
 
 
diff --git a/cirq-core/cirq/ops/gateset_test.py b/cirq-core/cirq/ops/gateset_test.py
index e09be035149..c7adc18c8b5 100644
--- a/cirq-core/cirq/ops/gateset_test.py
+++ b/cirq-core/cirq/ops/gateset_test.py
@@ -115,11 +115,21 @@ def test_invalid_gate_family():
 
 def test_gate_family_immutable():
     g = cirq.GateFamily(CustomX)
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    # Match one of two strings. The second one is message returned since python 3.11.
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'gate' of 'GateFamily' object has no setter)",
+    ):
         g.gate = CustomXPowGate
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'name' of 'GateFamily' object has no setter)",
+    ):
         g.name = 'new name'
-    with pytest.raises(AttributeError, match="can't set attribute"):
+    with pytest.raises(
+        AttributeError,
+        match="(can't set attribute)|(property 'description' of 'GateFamily' object has no setter)",
+    ):
         g.description = 'new description'
 
 
diff --git a/cirq-core/cirq/value/classical_data.py b/cirq-core/cirq/value/classical_data.py
index be8955c324a..b203b1e0c61 100644
--- a/cirq-core/cirq/value/classical_data.py
+++ b/cirq-core/cirq/value/classical_data.py
@@ -39,7 +39,7 @@ class MeasurementType(enum.IntEnum):
     CHANNEL = 2
 
     def __repr__(self):
-        return f'cirq.{str(self)}'
+        return f'cirq.MeasurementType.{self.name}'
 
 
 class ClassicalDataStoreReader(abc.ABC):