diff --git a/circuit_knitting/cutting/qpd/instructions/qpd_gate.py b/circuit_knitting/cutting/qpd/instructions/qpd_gate.py
index 7d2feac6e..555699d6b 100644
--- a/circuit_knitting/cutting/qpd/instructions/qpd_gate.py
+++ b/circuit_knitting/cutting/qpd/instructions/qpd_gate.py
@@ -201,6 +201,11 @@ def _define(self) -> None:
             qc.append(CircuitInstruction(op, [qc.qubits[0]], []))
         self.definition = qc
 
+    @property
+    def _directive(self):
+        """``True`` if the ``basis_id`` is unassigned, which implies this instruction cannot be decomposed."""
+        return self.basis_id is None
+
     def __eq__(self, other):
         """Check equivalence for SingleQubitQPDGate class."""
         return super().__eq__(other) and self.qubit_id == other.qubit_id
diff --git a/test/cutting/test_cutting_workflows.py b/test/cutting/test_cutting_workflows.py
new file mode 100644
index 000000000..b202c6ad0
--- /dev/null
+++ b/test/cutting/test_cutting_workflows.py
@@ -0,0 +1,50 @@
+# This code is a Qiskit project.
+
+# (C) Copyright IBM 2023.
+
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Tests of various cutting workflows, particularly with regard to flexibility in transpilation."""
+
+from copy import deepcopy
+
+from qiskit.circuit.library import EfficientSU2, CXGate
+from qiskit.quantum_info import PauliList
+from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager
+from qiskit.providers.fake_provider import FakeLagosV2
+
+from circuit_knitting.cutting.qpd.instructions import SingleQubitQPDGate
+from circuit_knitting.cutting.qpd import QPDBasis
+from circuit_knitting.cutting import partition_problem
+
+
+def test_transpile_before_realizing_basis_id():
+    """Test a workflow where a :class:`.SingleQubitQPDGate` is passed through the transpiler."""
+    circuit = EfficientSU2(4, entanglement="linear", reps=2).decompose()
+    circuit.assign_parameters([0.8] * len(circuit.parameters), inplace=True)
+    observables = PauliList(["ZZII"])
+    subcircuits, bases, subobservables = partition_problem(
+        circuit=circuit, partition_labels="AABB", observables=observables
+    )
+
+    # Create a fake backend, and modify the target gate set so it thinks a
+    # SingleQubitQPDGate is allowed.
+    backend = FakeLagosV2()
+    target = deepcopy(backend.target)
+    sample_qpd_instruction = SingleQubitQPDGate(QPDBasis.from_gate(CXGate()), 1)
+    target.add_instruction(
+        sample_qpd_instruction,
+        {(i,): None for i in range(target.num_qubits)},
+    )
+    pass_manager = generate_preset_pass_manager(3, target=target)
+
+    # Pass each subcircuit through the pass manager.
+    subcircuits = {
+        label: pass_manager.run(subcircuits["A"])
+        for label, circuit in subcircuits.items()
+    }