diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index e88995d..554fa7a 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -145,7 +145,10 @@ jobs:
           pip install -U pip
           pip install -U setuptools wheel twine cffi
 
-      - name: Build zope.security
+      - name: Build zope.security (Python 3.10 on MacOS)
+        if: >
+          startsWith(runner.os, 'Mac')
+          && startsWith(matrix.python-version, '3.10')
         env:
           _PYTHON_HOST_PLATFORM: macosx-11-x86_64
         run: |
@@ -157,6 +160,19 @@ jobs:
           pip install -U 'faulthandler; python_version == "2.7" and platform_python_implementation == "CPython"'
           pip install --pre .[test]
 
+      - name: Build zope.security (all other versions)
+        if: >
+          !startsWith(runner.os, 'Mac')
+          || !startsWith(matrix.python-version, '3.10')
+        run: |
+          # Next, build the wheel *in place*. This helps ccache, and also lets us cache the configure
+          # output (pip install uses a random temporary directory, making this difficult).
+          python setup.py build_ext -i
+          python setup.py bdist_wheel
+          # Also install it, so that we get dependencies in the (pip) cache.
+          pip install -U 'faulthandler; python_version == "2.7" and platform_python_implementation == "CPython"'
+          pip install --pre .[test]
+
       - name: Check zope.security build
         run: |
           ls -l dist
@@ -321,7 +337,7 @@ jobs:
         run: |
           pip install -U wheel
           pip install -U coverage
-          pip install -U  "`ls dist/zope.security-${{ runner.os }}-${{ matrix.python-version }}.whl`[docs]"
+          pip install -U  "`ls dist/zope.security-*.whl`[docs]"
       - name: Build docs
         env:
           ZOPE_INTERFACE_STRICT_IRO: 1
@@ -372,7 +388,7 @@ jobs:
         run: |
           pip install -U pip
           pip install -U wheel
-          pip install -U `ls dist/zope.security-${{ runner.os }}-${{ matrix.python-version }}`[test]
+          pip install -U `ls dist/zope.security-*`[test]
       - name: Lint
         # We only need to do this on one version, and it should be Python 3, because
         # pylint has stopped updating for Python 2.