diff --git a/qiskit/transpiler/passes/optimization/optimize_1q_decomposition.py b/qiskit/transpiler/passes/optimization/optimize_1q_decomposition.py
index f96ed999061d..9eb31b8f8134 100644
--- a/qiskit/transpiler/passes/optimization/optimize_1q_decomposition.py
+++ b/qiskit/transpiler/passes/optimization/optimize_1q_decomposition.py
@@ -173,10 +173,16 @@ def _substitution_checks(self, dag, old_run, new_circ, basis, qubit):
         # if we're outside of the basis set, we're obligated to logically decompose.
         # if we're outside of the set of gates for which we have physical definitions,
         #    then we _try_ to decompose, using the results if we see improvement.
+        new_error = 0.0
+        old_error = 0.0
+        if not uncalibrated_and_not_basis_p:
+            new_error = self._error(new_circ, qubit)
+            old_error = self._error(old_run, qubit)
+
         return (
             uncalibrated_and_not_basis_p
-            or (uncalibrated_p and self._error(new_circ, qubit) < self._error(old_run, qubit))
-            or math.isclose(self._error(new_circ, qubit)[0], 0)
+            or (uncalibrated_p and new_error < old_error)
+            or (math.isclose(new_error[0], 0) and not math.isclose(old_error[0], 0))
         )
 
     @control_flow.trivial_recurse
diff --git a/releasenotes/notes/fix-optimize-1q-sim-407b88e45e6062b6.yaml b/releasenotes/notes/fix-optimize-1q-sim-407b88e45e6062b6.yaml
new file mode 100644
index 000000000000..f531561789e0
--- /dev/null
+++ b/releasenotes/notes/fix-optimize-1q-sim-407b88e45e6062b6.yaml
@@ -0,0 +1,10 @@
+---
+fixes:
+  - |
+    Fixed an issue with the :class:`.Optimize1qGatesDecomposition` transpiler
+    pass where it would potentially resynthesize a single ideal (meaning the
+    error rate is ``0.0``) gate which was present in the :class:`.Target`. This
+    is now fixed so the pass :class:`.Optimize1qGatesDecomposition` will defer
+    to the circuit's gate if the error rate (which includes number of gates)
+    are the same.
+    Fixed `#10568 <https://github.com/Qiskit/qiskit/issues/10568>`__
diff --git a/test/python/transpiler/test_optimize_1q_decomposition.py b/test/python/transpiler/test_optimize_1q_decomposition.py
index 5d3ebb3d7245..72dbae0d3115 100644
--- a/test/python/transpiler/test_optimize_1q_decomposition.py
+++ b/test/python/transpiler/test_optimize_1q_decomposition.py
@@ -745,6 +745,20 @@ def test_nested_control_flow(self):
         result = passmanager.run(test)
         self.assertEqual(result, expected)
 
+    def test_prefer_no_substitution_if_all_ideal(self):
+        """Test that gates are not substituted if all our ideal gates in basis."""
+        target = Target(num_qubits=1)
+        target.add_instruction(HGate(), {(0,): InstructionProperties(error=0)})
+        target.add_instruction(
+            UGate(Parameter("a"), Parameter("b"), Parameter("c")),
+            {(0,): InstructionProperties(error=0)},
+        )
+        qc = QuantumCircuit(1)
+        qc.h(0)
+        opt_pass = Optimize1qGatesDecomposition(target)
+        res = opt_pass(qc)
+        self.assertEqual(res, qc)
+
 
 if __name__ == "__main__":
     unittest.main()