diff --git a/.travis.yml b/.travis.yml
index 0d739f6d..99bbd062 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,6 +4,13 @@ python:
   - "3.6"
   - "3.7"
   - "3.8"
+jobs:
+  include:
+    - python: "3.5"
+      env: TOXENV=py35-oldbs4
+  allow_failures:
+    - python: "3.5"
+      env: TOXENV=py35-oldbs4
 # command to install dependencies
 addons:
   apt:
diff --git a/tox.ini b/tox.ini
index 6a3bf312..e1ca67a4 100644
--- a/tox.ini
+++ b/tox.ini
@@ -31,3 +31,8 @@ deps =
     dnspython
     future
     {[base]deps}
+
+[travis]
+# don't run py35-oldbs4 by default in the Python 3.5 job
+python =
+  3.5: py35