diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 61ab393..d01a64f 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -41,12 +41,29 @@ jobs:
     steps:
       - uses: actions/checkout@v3
 
+      - name: Set up Python 3.7 to bootstrap py3.6 and py3.5
+        if: ${{ matrix.python-version == '3.6' or matrix.python-version == '3.5' }}
+        uses: actions/setup-python@v4
+        with:
+          python-version: 3.7
+
       - name: Set up Python ${{ matrix.python-version }}
         uses: actions/setup-python@v4
         with:
           python-version: ${{ matrix.python-version }}
 
+      # Python 3.6 & 3.7 cannot install directly from a pyproject.toml
+      # Instead, build a wheel from py3.7 and then install it
+      - name: Install via wheel
+        if: ${{ matrix.python-version == '3.6' or matrix.python-version == '3.5' }}
+        run: |
+          python3.7 -m pip install build
+          python3.7 -m build
+          python --version
+          python -m pip install ./dist/*.whl
+
       - name: Install
+        if: ${{ matrix.python-version != '3.6' and matrix.python-version != '3.5' }}
         run: |
           python -m pip install .