diff --git a/.github/workflows/publish-pypi.yml b/.github/workflows/publish-pypi.yml
index b5db15e..513a80f 100644
--- a/.github/workflows/publish-pypi.yml
+++ b/.github/workflows/publish-pypi.yml
@@ -103,7 +103,6 @@ jobs:
             platform_id: macosx_x86_64
             deployment_target: 13.0
 
-
           # MacOS ARM
           - os: macos-14
             python: 310
@@ -138,12 +137,14 @@ jobs:
       - name: Checkout CPT
         uses: actions/checkout@v3
 
-      - name: Setup Python
-        uses: actions/setup-python@v5
-        with:
-          python-version: '3.13'
+      - name: macOS OpenMP setup
+        if: runner.os == 'macOS'
+        run: bash CI/github/setup_macos_runner.sh
 
-      - name: Build and test wheels
+      - name: Build wheels
+        uses: pypa/cibuildwheel@v3.1.2
+        with:
+          output-dir: wheelhouse
         env:
           CIBW_BEFORE_BUILD: "python -m pip install --upgrade pip"
           CIBW_BUILD: cp${{ matrix.python }}-${{ matrix.platform_id }}
@@ -157,8 +158,6 @@ jobs:
           CIBW_ENVIRONMENT_MACOS: ${{ format('MACOSX_DEPLOYMENT_TARGET={0}', matrix.deployment_target) }}
           CIBW_ENABLE: cpython-freethreading
 
-        run: bash CI/github/build_wheels.sh
-
       - name: Store artifacts
         uses: actions/upload-artifact@v4
         with:
diff --git a/CI/github/build_wheels.sh b/CI/github/setup_macos_runner.sh
old mode 100755
new mode 100644
similarity index 74%
rename from CI/github/build_wheels.sh
rename to CI/github/setup_macos_runner.sh
index 695ddfa..cdc8da7
--- a/CI/github/build_wheels.sh
+++ b/CI/github/setup_macos_runner.sh
@@ -4,7 +4,7 @@ set -e
 set -x
 
 # OpenMP is not present on macOS by default
-if [[ "$RUNNER_OS" == "macOS" ]]; then
+if [[ "$RUNNER_OS" == "macOS" ]]; then # this if is useless, but better be safe
     echo "Installing Mac OS dependencies"
 	brew_prefix=$(brew --prefix)
     brew install libomp
@@ -15,7 +15,3 @@ if [[ "$RUNNER_OS" == "macOS" ]]; then
     export CXXFLAGS="$CXXFLAGS -I$brew_prefix/opt/libomp/include"
     export LDFLAGS="$LDFLAGS -Wl,-rpath,$brew_prefix/opt/libomp/lib -L$brew_prefix/opt/libomp/lib -lomp"
 fi
-
-python -m pip install cibuildwheel==3.1.1
-python -m cibuildwheel --print-build-identifiers
-python -m cibuildwheel --output-dir wheelhouse