diff --git a/.github/workflows/python-build-package.yml b/.github/workflows/python-build-package.yml
index 7f48420c..0d209ea1 100644
--- a/.github/workflows/python-build-package.yml
+++ b/.github/workflows/python-build-package.yml
@@ -86,9 +86,64 @@ jobs:
       - name: Upload wheels
         uses: actions/upload-artifact@v4
         with:
-          name: wheels-${{ matrix.platform.runner }}-${{ matrix.platform.target }}
+          name: wheel-${{ matrix.platform.runner }}-${{ matrix.platform.target }}
           path: dist
 
+  # Download, install, and test the wheels with different versions of python
+  test-wheels:
+    needs: [build-wheels]
+    runs-on: ${{ matrix.platform.runner }}
+    strategy:
+      # We want to know in which exact situation the tests fail
+      fail-fast: false
+      matrix:
+        python-version: [ "3.8", "3.9", "3.10", "3.11", "3.12" ]
+        platform:
+          - runner: ubuntu-latest
+            target: x86_64
+          - runner: windows-latest
+            target: x64
+          - runner: macos-14
+            target: aarch64
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/download-artifact@v4
+        with:
+          name: wheel-${{ matrix.platform.runner }}-${{ matrix.platform.target }}
+          path: dist
+      - name: Setup Python
+        uses: actions/setup-python@0b93645e9fea7318ecaed2b359559ac225c90a2b # pin@v5
+        with:
+          python-version: '${{ matrix.python-version }}'
+      - name: Install uv
+        run: curl -LsSf https://astral.sh/uv/0.5.22/install.sh | sh
+      - if: matrix.platform.runner != 'windows-latest'
+        name: Check that `uv add magika.whl` works
+        run: |
+          mkdir /tmp/test-uv
+          cp -vR dist/*.whl /tmp/test-uv
+          cd /tmp/test-uv
+          uv init
+          uv add ./$(\ls -1 *.whl | head -n 1)
+      - if: matrix.platform.runner == 'windows-latest'
+        name: Check that `uv add magika.whl` works
+        shell: pwsh
+        run: |
+          mkdir C:\test-uv
+          Copy-Item -Path dist\*.whl -Destination C:\test-uv
+          cd C:\test-uv
+          $env:PATH += ";$HOME/.local/bin"
+          uv init
+          $wheel = Get-ChildItem -Filter *.whl | Select-Object -ExpandProperty Name
+          uv add ".\$wheel"
+      - name: Install the wheel
+        run: python3 -m pip install $(python -c "import glob; print(glob.glob('dist/*.whl')[0])")
+      - run: magika --version
+      - run: "python3 -c 'import magika; m = magika.Magika(); print(m)'"
+      - run: magika -r tests_data/basic
+      - run: python3 ./python/scripts/run_quick_test_magika_cli.py
+      - run: python3 ./python/scripts/run_quick_test_magika_module.py
+
   build-pure-python-wheel:
     runs-on: ubuntu-latest
     steps:
@@ -117,7 +172,7 @@ jobs:
       - name: Upload wheel
         uses: actions/upload-artifact@v4
         with:
-          name: wheels-pure-python
+          name: wheel-pure-python
           path: dist
 
   # Download, install, and test the pure python wheel on multiple platforms
@@ -125,7 +180,10 @@ jobs:
     needs: [build-pure-python-wheel]
     runs-on: ${{ matrix.platform.runner }}
     strategy:
+      # We want to know in which exact situation the tests fail
+      fail-fast: false
       matrix:
+        python-version: [ "3.8", "3.9", "3.10", "3.11", "3.12" ]
         platform:
           - runner: ubuntu-latest
             target: x86_64
@@ -137,12 +195,12 @@ jobs:
       - uses: actions/checkout@v4
       - uses: actions/download-artifact@v4
         with:
-          name: wheels-pure-python
+          name: wheel-pure-python
           path: dist
       - name: Setup Python
         uses: actions/setup-python@0b93645e9fea7318ecaed2b359559ac225c90a2b # pin@v5
         with:
-          python-version: '3.12'
+          python-version: '${{ matrix.python-version }}'
       - name: Install uv
         run: curl -LsSf https://astral.sh/uv/0.5.22/install.sh | sh
       - if: matrix.platform.runner != 'windows-latest'