diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 42c76251..e477bece 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -259,9 +259,9 @@ def setup_python(python_configuration: PythonConfiguration,
                 # set ARCHFLAGS otherwise CPython sets it to `-arch x86_64`
                 env.setdefault('ARCHFLAGS', '-arch arm64 -arch x86_64')
 
-    if python_configuration.identifier.endswith('_arm64') or python_configuration.identifier.endswith('_universal2'):
+    if python_configuration.identifier.endswith('arm64') or python_configuration.identifier.endswith('universal2'):
         if get_macos_version() < (10, 16):
-            # xcode 12 or higher can build arm64 on macos 10.15 or below, but
+            # xcode 12.2 or higher can build arm64 on macos 10.15 or below, but
             # needs the correct SDK selected
 
             # however, different versions of Xcode contain different SDK
diff --git a/docs/faq.md b/docs/faq.md
index da8bc522..95a99be9 100644
--- a/docs/faq.md
+++ b/docs/faq.md
@@ -58,7 +58,7 @@ These wheels are not built by default, but can be enabled by setting the [`CIBW_
 Hopefully, this is a temporary situation. Once we have widely available Apple Silicon CI runners, we can build and test `arm64` and `universal2` wheels more natively. That's why `universal2` wheels are not yet built by default, and require opt-in by setting `CIBW_ARCHS_MACOS`.
 
 !!! note
-    Your runner image needs Xcode Command Line Tools 12 or later to build `universal2` and `arm64`.
+    Your runner image needs Xcode Command Line Tools 12.2 or later to build `universal2` and `arm64`.
 
     So far, only CPython 3.9 supports `universal2` and `arm64` wheels.
 
diff --git a/docs/options.md b/docs/options.md
index f255cf28..dc46a110 100644
--- a/docs/options.md
+++ b/docs/options.md
@@ -186,6 +186,8 @@ Default: `auto`
 | macOS / Intel | `x86_64` | `x86_64`
 | macOS / Apple Silicon | `arm64` | `arm64` `universal2`
 
+If not listed above, `auto` is the same as `native`.
+
 [setup-qemu-action]: https://github.com/docker/setup-qemu-action
 [binfmt]: https://hub.docker.com/r/tonistiigi/binfmt
 
diff --git a/test/test_macos_archs.py b/test/test_macos_archs.py
index bd26a42e..de2ada1c 100644
--- a/test/test_macos_archs.py
+++ b/test/test_macos_archs.py
@@ -29,8 +29,8 @@ def get_xcode_version() -> Tuple[int, int]:
 def test_cross_compiled_build(tmp_path):
     if utils.platform != 'macos':
         pytest.skip('this test is only relevant to macos')
-    if get_xcode_version() < (12, 0):
-        pytest.skip('this test only works with Xcode 12 or greater')
+    if get_xcode_version() < (12, 2):
+        pytest.skip('this test only works with Xcode 12.2 or greater')
 
     project_dir = tmp_path / 'project'
     basic_project.generate(project_dir)
@@ -48,8 +48,8 @@ def test_cross_compiled_build(tmp_path):
 def test_cross_compiled_test(tmp_path, capfd, build_universal2):
     if utils.platform != 'macos':
         pytest.skip('this test is only relevant to macos')
-    if get_xcode_version() < (12, 0):
-        pytest.skip('this test only works with Xcode 12 or greater')
+    if get_xcode_version() < (12, 2):
+        pytest.skip('this test only works with Xcode 12.2 or greater')
 
     project_dir = tmp_path / 'project'
     basic_project.generate(project_dir)
@@ -87,8 +87,8 @@ def test_cross_compiled_test(tmp_path, capfd, build_universal2):
 def test_universal2_testing(tmp_path, capfd, skip_arm64_test):
     if utils.platform != 'macos':
         pytest.skip('this test is only relevant to macos')
-    if get_xcode_version() < (12, 0):
-        pytest.skip('this test only works with Xcode 12 or greater')
+    if get_xcode_version() < (12, 2):
+        pytest.skip('this test only works with Xcode 12.2 or greater')
     if platform.machine() != 'x86_64':
         pytest.skip('this test only works on x86_64')