diff --git a/tox.ini b/tox.ini
index 788af31..6772f9d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,10 +1,15 @@
 [tox]
-minversion = 3.7
+minversion = 3.23
 envlist =
-    py27,py36,py37,py38,py39,py310,py311,pypy2,pypy3
+    py{38,39,310,311}
+    pypy{38,310}
+    eol_py{27,36,37,py27}
     cover-{clean,report}
     lint
 
+labels =
+    eol = eol_py{27,36,37,py27}
+
 [gh-actions]
 python =
     2.7: py27
@@ -12,8 +17,11 @@ python =
     3.7: py37
     3.8: py38
     3.9: py39
-    pypy-2.7: pypy2
-    pypy-3.7: pypy3
+    3.10: py310
+    3.11: py311
+    pypy-2.7: pypy27
+    pypy-3.8: pypy38
+    pypy-3.10: pypy310
 
 [testenv]
 deps =
@@ -24,8 +32,9 @@ commands =
     pytest --doctest-modules --doctest-glob=README.md README.md src
 
 depends:
-    py27,py36,py37,py38,py39,py310,py311,pypy2,pypy3: cover-clean
-    cover-report: py27,py36,py37,py38,py39,py310,py311,pypy2,pypy3
+    py{38,39,310,311},pypy{27,38,310}: cover-clean
+    cover-report: py{38,39,310,311},pypy{27,38,310}
+
 
 [testenv:cover-clean]
 skip_install = true
@@ -50,6 +59,41 @@ commands =
     twine check {envtmpdir}/dist/*
     check-manifest
 
+# Old versions of tox & virtualenv are required to test under eol
+# versions of python.  However, those old versions don't seem to
+# consistently work with newer pythons, e.g. pypy310.
+#
+# So this hack...
+[eoltox]
+deps =
+    tox<4
+    virtualenv<20.22.0
+    setuptools
+
+[testenv:eol_py27]
+skip_install = true
+deps = {[eoltox]deps}
+commands =
+    tox -e py27
+
+[testenv:eol_py36]
+skip_install = true
+deps = {[eoltox]deps}
+commands =
+    tox -e py36
+
+[testenv:eol_py37]
+skip_install = true
+deps = {[eoltox]deps}
+commands =
+    tox -e py37
+
+[testenv:eol_pypy27]
+skip_install = true
+deps = {[eoltox]deps}
+commands =
+    tox -e pypy27
+
 [flake8]
 # because black
 max-line-length = 88