diff --git a/.github/workflows/cygwin-test.yml b/.github/workflows/cygwin-test.yml
index d42eb0587..bc1c34e1d 100644
--- a/.github/workflows/cygwin-test.yml
+++ b/.github/workflows/cygwin-test.yml
@@ -7,6 +7,16 @@ jobs:
     runs-on: windows-latest
 
     strategy:
+      matrix:
+        python-version: ["3.9", "3.12"]
+        include:
+        - python-version: "3.9"
+          python-cygwin: python39
+          venv-args: ''
+        - python-version: "3.12"
+          python-cygwin: python312
+          venv-args: --without-pip
+
       fail-fast: false
 
     env:
@@ -30,7 +40,7 @@ jobs:
     - name: Set up Cygwin
       uses: egor-tensin/setup-cygwin@v4
       with:
-        packages: python39 python39-pip python39-virtualenv git
+        packages: ${{ matrix.python-cygwin }} ${{ matrix.python-cygwin }}-pip ${{ matrix.python-cygwin }}-virtualenv git wget
 
     - name: Arrange for verbose output
       run: |
@@ -57,9 +67,14 @@ jobs:
 
     - name: Set up virtualenv
       run: |
-        python -m venv .venv
+        python${{ matrix.python-version }} -m venv ${{ matrix.venv-args }} .venv
         echo 'BASH_ENV=.venv/bin/activate' >>"$GITHUB_ENV"
 
+    - name: Bootstrap pip in virtualenv
+      if: contains(matrix.venv-args, '--without-pip')
+      run: |
+        wget -qO- https://bootstrap.pypa.io/get-pip.py | python
+
     - name: Update PyPA packages
       run: |
         # Get the latest pip, wheel, and prior to Python 3.12, setuptools.