diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 4cc5a67..809af7c 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -2,38 +2,38 @@
     sha: 003e43251aea1da33f2072f2365ec8b9ceaae070
     hooks:
     -   id: autopep8-wrapper
-        language_version: python3.5
+        language_version: python3.6
     -   id: check-added-large-files
-        language_version: python3.5
+        language_version: python3.6
     -   id: check-docstring-first
-        language_version: python3.5
+        language_version: python3.6
     -   id: check-merge-conflict
-        language_version: python3.5
+        language_version: python3.6
     -   id: check-yaml
-        language_version: python3.5
+        language_version: python3.6
     -   id: debug-statements
-        language_version: python3.5
+        language_version: python3.6
     -   id: detect-private-key
-        language_version: python3.5
+        language_version: python3.6
     -   id: double-quote-string-fixer
-        language_version: python3.5
+        language_version: python3.6
     -   id: end-of-file-fixer
-        language_version: python3.5
+        language_version: python3.6
     -   id: flake8
-        language_version: python3.5
+        language_version: python3.6
     -   id: name-tests-test
-        language_version: python3.5
+        language_version: python3.6
     -   id: requirements-txt-fixer
-        language_version: python3.5
+        language_version: python3.6
     -   id: trailing-whitespace
-        language_version: python3.5
+        language_version: python3.6
 -   repo: https://github.com/asottile/reorder_python_imports.git
     sha: 3d86483455ab5bd06cc1069fdd5ac57be5463f10
     hooks:
     -   id: reorder-python-imports
-        language_version: python3.5
+        language_version: python3.6
 -   repo: https://github.com/Lucas-C/pre-commit-hooks.git
     sha: 181a63c511691da58116fa19a7241956018660bc
     hooks:
     -   id: remove-tabs
-        language_version: python3.5
+        language_version: python3.6
diff --git a/Dockerfile b/Dockerfile
index 7cc4f3d..3f69ddb 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -2,6 +2,11 @@ FROM debian:stretch
 
 MAINTAINER Chris Kuehl <ckuehl@yelp.com>
 
+# The default mirrors are too flaky to run reliably in CI.
+RUN sed -E \
+    '/security\.debian/! s@http://[^/]+/@http://mirrors.kernel.org/@' \
+    -i /etc/apt/sources.list
+
 # Install the bare minimum dependencies necessary for working with Debian
 # packages. Build dependencies should be added under "Build-Depends" inside
 # debian/control instead.
diff --git a/ci/docker b/ci/docker
index fb725e4..a07c27f 100644
--- a/ci/docker
+++ b/ci/docker
@@ -2,6 +2,11 @@ if grep -qE '\<lucid\>' /etc/apt/sources.list; then
     # lucid was archived, breaking the base image
     # https://github.com/docker-library/official-images/issues/1902
     sed -i 's/archive\.ubuntu\.com/old-releases.ubuntu.com/g' /etc/apt/sources.list
+else
+    # The default mirrors are too flaky to run reliably in CI.
+    sed -E \
+        '/security\.debian/! s@http://[^/]+/@http://mirrors.kernel.org/@' \
+        -i /etc/apt/sources.list
 fi
 
 apt-get update
diff --git a/ci/docker-tox b/ci/docker-tox
index 9907bc8..2a81020 100644
--- a/ci/docker-tox
+++ b/ci/docker-tox
@@ -3,15 +3,21 @@ set -o pipefail
 
 . /mnt/ci/docker
 
+# The default mirrors are too flaky to run reliably in CI.
+sed -E \
+    '/security\.debian/! s@http://[^/]+/@http://mirrors.kernel.org/@' \
+    -i /etc/apt/sources.list
+
 apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 0x5BB92C09DB82666C
 echo 'deb http://ppa.launchpad.net/fkrull/deadsnakes/ubuntu xenial main' >> /etc/apt/sources.list
+
 apt-get update
 apt-get install -y --no-install-recommends \
     git \
     python2.6-dev \
     python2.7-dev \
-    python3.4-dev \
-    python3.5-dev
+    python3.5-dev \
+    python3.6-dev
 
 # We cannot use the Ubuntu versions of tox or virtualenv:
 # https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=754248
diff --git a/tox.ini b/tox.ini
index 55b98ab..f6967e9 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py26,py27,py34,py35
+envlist = py26,py27,py35,py36
 
 [testenv]
 deps = -r{toxinidir}/requirements-dev.txt