diff --git a/.buildkite/scripts/test_old_deps.sh b/.buildkite/scripts/test_old_deps.sh
index 9fe5b696b..3753f41a4 100755
--- a/.buildkite/scripts/test_old_deps.sh
+++ b/.buildkite/scripts/test_old_deps.sh
@@ -1,16 +1,16 @@
 #!/usr/bin/env bash
 
 # this script is run by buildkite in a plain `xenial` container; it installs the
-# minimal requirements for tox and hands over to the py35-old tox environment.
+# minimal requirements for tox and hands over to the py3-old tox environment.
 
 set -ex
 
 apt-get update
-apt-get install -y python3.5 python3.5-dev python3-pip libxml2-dev libxslt-dev xmlsec1 zlib1g-dev tox
+apt-get install -y python3 python3-dev python3-pip libxml2-dev libxslt-dev xmlsec1 zlib1g-dev tox
 
 export LANG="C.UTF-8"
 
 # Prevent virtualenv from auto-updating pip to an incompatible version
 export VIRTUALENV_NO_DOWNLOAD=1
 
-exec tox -e py35-old,combine
+exec tox -e py3-old,combine
diff --git a/tox.ini b/tox.ini
index 8224edaef..b2bc6f23e 100644
--- a/tox.ini
+++ b/tox.ini
@@ -74,7 +74,7 @@ commands =
     # we use "env" rather than putting a value in `setenv` so that it is not
     # inherited by other tox environments.
     #
-    # keep this in sync with the copy in `testenv:py35-old`.
+    # keep this in sync with the copy in `testenv:py3-old`.
     #
     /usr/bin/env COVERAGE_PROCESS_START={toxinidir}/.coveragerc "{envbindir}/trial" {env:TRIAL_FLAGS:} {posargs:tests} {env:TOXSUFFIX:}
 
@@ -103,7 +103,7 @@ usedevelop=true
 
 # A test suite for the oldest supported versions of Python libraries, to catch
 # any uses of APIs not available in them.
-[testenv:py35-old]
+[testenv:py3-old]
 skip_install = true
 usedevelop = false
 deps =