diff --git a/src/qc_compiler/cost_model.py b/src/qc_compiler/cost_model.py
index fd49dcd..3ff22e7 100644
--- a/src/qc_compiler/cost_model.py
+++ b/src/qc_compiler/cost_model.py
@@ -475,7 +475,7 @@ def _get_measured_qubits(self, circuit: QuantumCircuit) -> list[int]:
                 for qubit in instr.qubits:
                     measured.add(circuit.find_bit(qubit).index)
         if not measured:
-            measured = set(range(circuit.num_qubits))
+            return []
         return sorted(measured)
 
     def estimate_fidelity(
diff --git a/tests/test_cost_model.py b/tests/test_cost_model.py
index 1b85e70..d67e572 100644
--- a/tests/test_cost_model.py
+++ b/tests/test_cost_model.py
@@ -167,7 +167,24 @@ def test_measurement_error_no_measure(self):
         qc.h(0)
         qc.cx(0, 1)
         error = model.estimate_measurement_error(qc)
+        assert error == 0.0
+
+    def test_measurement_error_only_measured_qubits(self):
+        model = CostModel()
+        device = DeviceCharacterization(
+            backend_name="test",
+            num_qubits=3,
+            readout_errors={0: 0.01, 1: 0.02, 2: 0.03},
+        )
+        model = CostModel()
+        model.device = device
+        qc = QuantumCircuit(3, 1)
+        qc.h(0)
+        qc.cx(0, 1)
+        qc.measure(0, 0)
+        error = model.estimate_measurement_error(qc)
         assert error > 0
+        assert error < 0.02
 
     def test_fidelity_bell_state(self):
         model = CostModel()