diff --git a/.htmltest.yml b/.htmltest.yml
index f7afd545..c61aceaf 100644
--- a/.htmltest.yml
+++ b/.htmltest.yml
@@ -1,6 +1,8 @@
 IgnoreAltMissing: true
 IgnoreURLs:
   - "^http://localhost:"
+  # For unknown reasons, htmltest reports a 404 on these one:
+  - "^https://twitter.com/"
 
 # htmltest does not like quotes around URL in meta refresh
 CheckMetaRefresh: false
diff --git a/tox.ini b/tox.ini
index 58f0faaa..4b732d7b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,12 +1,37 @@
 [tox]
-minversion = 3
-envlist = py
+minversion = 3.18
+envlist = build
 skipsdist = true
 
 [testenv]
 deps =
     lektor
-    jinja2>=3
+setenv =
+    # Keep Lektor's private package cache in tox env rather than ~/.cache
+    XDG_CACHE_HOME = {envdir}/cache
+    LOCALAPPDATA = {envdir}/cache
+
+[testenv:build]
 commands =
-    lektor plugins reinstall
-    lektor build
+    lektor build -O {envdir}/output
+
+[testenv:htmltest]
+# Build site and check links with htmltest
+#
+# By default, only internal links are checked.
+#
+#     tox -e htmltest
+#
+# To test external links as well, try (warning: slow):
+#
+#     HTMLTEST_OPTS="" tox -e htmltest
+#
+allowlist_externals =
+    bash
+commands_pre =
+    # Install latest version of htmltest in the tox env
+    bash -c '[ -f {envbindir}/htmltest ] || \
+             curl -s https://htmltest.wjdp.uk | bash -s -- -b {envbindir}'
+commands =
+    {[testenv:build]commands}
+    htmltest -c .htmltest.yml {env:HTMLTEST_OPTS:-s} {envdir}/output