diff --git a/qiskit/transpiler/passes/synthesis/unitary_synthesis.py b/qiskit/transpiler/passes/synthesis/unitary_synthesis.py
index 8e0ce6385eac..606df60869c9 100644
--- a/qiskit/transpiler/passes/synthesis/unitary_synthesis.py
+++ b/qiskit/transpiler/passes/synthesis/unitary_synthesis.py
@@ -35,6 +35,7 @@
 from qiskit.transpiler.exceptions import TranspilerError
 from qiskit.dagcircuit.dagcircuit import DAGCircuit
 from qiskit.synthesis.one_qubit import one_qubit_decompose
+from qiskit.transpiler.passes.optimization.optimize_1q_decomposition import _possible_decomposers
 from qiskit.synthesis.two_qubit.xx_decompose import XXDecomposer, XXEmbodiments
 from qiskit.synthesis.two_qubit.two_qubit_decompose import (
     TwoQubitBasisDecomposer,
@@ -84,23 +85,16 @@ def _choose_kak_gate(basis_gates):
 def _choose_euler_basis(basis_gates):
     """Choose the first available 1q basis to use in the Euler decomposition."""
     basis_set = set(basis_gates or [])
-
-    for basis, gates in one_qubit_decompose.ONE_QUBIT_EULER_BASIS_GATES.items():
-
-        if set(gates).issubset(basis_set):
-            return basis
-
+    decomposers = _possible_decomposers(basis_set)
+    if decomposers:
+        return decomposers[0]
     return "U"
 
 
 def _find_matching_euler_bases(target, qubit):
     """Find matching available 1q basis to use in the Euler decomposition."""
-    euler_basis_gates = []
     basis_set = target.operation_names_for_qargs((qubit,))
-    for basis, gates in one_qubit_decompose.ONE_QUBIT_EULER_BASIS_GATES.items():
-        if set(gates).issubset(basis_set):
-            euler_basis_gates.append(basis)
-    return euler_basis_gates
+    return _possible_decomposers(basis_set)
 
 
 def _choose_bases(basis_gates, basis_dict=None):
@@ -777,6 +771,13 @@ def is_controlled(gate):
             )
             decomposers.append(decomposer)
 
+        # If our 2q basis gates are a subset of cx, ecr, or cz then we know TwoQubitBasisDecomposer
+        # is an ideal decomposition and there is no need to bother calculating the XX embodiments
+        # or try the XX decomposer
+        if {"cx", "cz", "ecr"}.issuperset(available_2q_basis):
+            self._decomposer_cache[qubits_tuple] = decomposers
+            return decomposers
+
         # possible controlled decomposers (i.e. XXDecomposer)
         controlled_basis = {k: v for k, v in available_2q_basis.items() if is_controlled(v)}
         basis_2q_fidelity = {}