diff --git a/.github/workflows/build_wheels.yml b/.github/workflows/build_wheels.yml
index 3a6bcd1d..3d0205af 100644
--- a/.github/workflows/build_wheels.yml
+++ b/.github/workflows/build_wheels.yml
@@ -9,8 +9,9 @@ on:
   pull_request:
 
 env:
-  # Only support 64-bit CPython > 3.6
-  CIBW_SKIP: "cp36-* pp* *-manylinux_i686 *-musllinux_* *-win32 cp313-*"
+  # Only support 64-bit CPython >= 3.10
+  CIBW_BUILD: "cp310-* cp311-* cp312-* cp313-*"
+  CIBW_SKIP: "*-manylinux_i686 *-musllinux_* *-win32"
 
   # This has some of the software we need pre-installed on it
   CIBW_MANYLINUX_X86_64_IMAGE: openchemistry/stempy_wheel_builder_x86_64
@@ -23,12 +24,10 @@ env:
   CIBW_ENVIRONMENT_WINDOWS: >
     EXTRA_CMAKE_ARGS="-DEIGEN3_DIR=C:\\PROGRA~2\\Eigen3\\share\\eigen3\\cmake\\;-Dstempy_ENABLE_HDF5=OFF"
     USE_PYTHON_IN_PATH=1
-
   # Get cmake to use python in the path...
   CIBW_ENVIRONMENT_MACOS: >
     EXTRA_CMAKE_ARGS="-DHDF5_DIR=/usr/local/HDF_Group/HDF5/current/cmake"
     USE_PYTHON_IN_PATH=1
-
   CIBW_BEFORE_TEST: pip install -r {project}/tests/requirements.txt
 
   CIBW_TEST_COMMAND: pytest {project}/tests
@@ -64,7 +63,7 @@ jobs:
       - uses: actions/setup-python@v5
         name: Install Python
         with:
-          python-version: '3.10'
+          python-version: '3.12'
 
       - name: Install dependencies
         run: . .github/scripts/install.sh