diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 7ed90d5..a864d51 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -17,6 +17,15 @@ jobs:
         # https://raw.githubusercontent.com/actions/python-versions/main/versions-manifest.json
         python-version: [3.5, 3.6, 3.7, 3.8, 3.9, '3.10', '3.11.0-beta - 3.11', 'pypy-3.7', 'pypy-3.8', 'pypy-3.9']
         extra: ['', '-smtp']
+        # The forced pytest versions correspond with the lower bounds in tox.ini
+        pytest-version: ['', '--force-dep pytest==4', '--force-dep pytest==6.2.4']
+        exclude:
+          - python-version: '3.5'
+            pytest-version: '--force-dep pytest==6.2.4'
+          - python-version: '3.10'
+            pytest-version: '--force-dep pytest==4'
+          - python-version: '3.11.0-beta - 3.11'
+            pytest-version: '--force-dep pytest==4'
       fail-fast: false
 
     steps:
@@ -30,4 +39,4 @@ jobs:
         python -m pip install --upgrade pip
         pip install tox
     - name: Test with tox
-      run: tox -vv -e py${{ matrix.extra }}
+      run: tox -vv -e py${{ matrix.extra }} ${{ matrix.pytest-version }}
diff --git a/tox.ini b/tox.ini
index ebbd560..541ccf1 100644
--- a/tox.ini
+++ b/tox.ini
@@ -9,9 +9,21 @@ downloadcache = {toxworkdir}/_download
 [testenv]
 description = run test suite under {basepython}
 deps =
-    pytest >=4, <7; python_version<'3.10'
-    pytest >=6.2.5, <7; python_version>='3.10'
-#    pytest-cov >=2, <3
+    # Future major versions of pytest may break backwards compatibility in a way
+    # that prevents them from working with this package, so we prevent testing
+    # with major versions that haven't been released yet. Each time a new major
+    # version of pytest is released, once it's confirmed to work with this
+    # package, we should bump this limit to the next major version.
+    #
+    # The lower bounds come from testing with different pytest versions using
+    # tox's --force-dep option to find the earliest versions of pytest that are
+    # known to work. If you add code that breaks with an old version of pytest,
+    # feel free to raise these bounds to represent the earliest version that
+    # works with your code. Don't forget to modify the corresponding entries in
+    # the Github workflows configuration file if you do change these lower
+    # bounds.
+    pytest >=4, <8; python_version<'3.10'
+    pytest >=6.2.4, <8; python_version>='3.10'
     pytest-cov
     six
     requests