diff --git a/qiskit/dagcircuit/dagcircuit.py b/qiskit/dagcircuit/dagcircuit.py
index c5a97c09113f..01c99a13906c 100644
--- a/qiskit/dagcircuit/dagcircuit.py
+++ b/qiskit/dagcircuit/dagcircuit.py
@@ -786,17 +786,30 @@ def idle_wires(self, ignore=None):
 
         Yields:
             Bit: Bit in idle wire.
+
+        Raises:
+            DAGCircuitError: If the DAG is invalid
         """
         if ignore is None:
-            ignore = []
+            ignore = set()
+        ignore_set = set(ignore)
         for wire in self._wires:
-            nodes = [
-                node
-                for node in self.nodes_on_wire(wire, only_ops=True)
-                if node.op.name not in ignore
-            ]
-            if len(nodes) == 0:
-                yield wire
+            if not ignore:
+                try:
+                    child = next(self.successors(self.input_map[wire]))
+                except StopIteration as e:
+                    raise DAGCircuitError(
+                        "Invalid dagcircuit input node %s has no output" % self.input_map[wire]
+                    ) from e
+                if isinstance(child, DAGOutNode):
+                    yield wire
+            else:
+                for node in self.nodes_on_wire(wire, only_ops=True):
+                    if node.op.name not in ignore_set:
+                        # If we found an op node outside of ignore we can stop iterating over the wire
+                        break
+                else:
+                    yield wire
 
     def size(self):
         """Return the number of operations."""
diff --git a/qiskit/transpiler/passes/utils/remove_final_measurements.py b/qiskit/transpiler/passes/utils/remove_final_measurements.py
index 5bf156970203..35ad1eb6972f 100644
--- a/qiskit/transpiler/passes/utils/remove_final_measurements.py
+++ b/qiskit/transpiler/passes/utils/remove_final_measurements.py
@@ -34,25 +34,16 @@ def run(self, dag):
         Returns:
             DAGCircuit: the optimized DAG.
         """
-        final_op_types = ["measure", "barrier"]
+        final_op_types = {"measure", "barrier"}
         final_ops = []
         cregs_to_remove = dict()
         clbits_with_final_measures = set()
         clbit_registers = {clbit: creg for creg in dag.cregs.values() for clbit in creg}
 
-        for candidate_node in dag.named_nodes(*final_op_types):
-            is_final_op = True
-
-            for _, child_successors in dag.bfs_successors(candidate_node):
-                if any(
-                    isinstance(suc, DAGOpNode) and suc.name not in final_op_types
-                    for suc in child_successors
-                ):
-                    is_final_op = False
-                    break
-
-            if is_final_op:
-                final_ops.append(candidate_node)
+        for qubit in dag.qubits:
+            op_node = next(dag.predecessors(dag.output_map[qubit]))
+            if isinstance(op_node, DAGOpNode) and op_node.op.name in final_op_types:
+                final_ops.append(op_node)
 
         if not final_ops:
             return dag
@@ -77,10 +68,4 @@ def run(self, dag):
             if val in cregs_to_remove and cregs_to_remove[val] == val.size:
                 del dag.cregs[key]
 
-        new_dag = dag._copy_circuit_metadata()
-
-        for node in dag.topological_op_nodes():
-            # copy the condition over too
-            new_dag.apply_operation_back(node.op, qargs=node.qargs, cargs=node.cargs)
-
-        return new_dag
+        return dag