diff --git a/.travis.yml b/.travis.yml
index 5aefc99..c783887 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -14,19 +14,16 @@
     - python: pypy
     - os: osx
       language: generic
-      env: PYTHON=3.7.2 TOXENV=py37
+      env: CONDA=3.7 TOXENV=py37
     - os: osx
       language: generic
-      env: PYTHON=3.6.8 TOXENV=py36
+      env: CONDA=3.6 TOXENV=py36
     - os: osx
       language: generic
-      env: PYTHON=3.5.6 TOXENV=py35
+      env: CONDA=3.5 TOXENV=py35
     - os: osx
       language: generic
-      env: PYTHON=3.4.9 TOXENV=py34
-    - os: osx
-      language: generic
-      env: PYTHON=2.7.15 TOXENV=py27
+      env: CONDA=2.7 TOXENV=py27
 
   allow_failures:
     - env: OPTIONAL=1
@@ -34,24 +31,16 @@
   fast_finish: true
 
 before_install: |
-  if [ "$TRAVIS_OS_NAME" == "osx" ]; then
-    brew update
-    # Per the `pyenv homebrew recommendations <https://github.com/yyuu/pyenv/wiki#suggested-build-environment>`_.
-    brew install openssl readline
-    # See https://docs.travis-ci.com/user/osx-ci-environment/#A-note-on-upgrading-packages.
-    # I didn't do this above because it works and I'm lazy.
-    brew outdated pyenv || brew upgrade pyenv
-    # virtualenv doesn't work without pyenv knowledge. venv in Python 3.3
-    # doesn't provide Pip by default. So, use `pyenv-virtualenv <https://github.com/yyuu/pyenv-virtualenv/blob/master/README.md>`_.
-    brew install pyenv-virtualenv
-    pyenv install $PYTHON
-    # I would expect something like ``pyenv init; pyenv local $PYTHON`` or
-    # ``pyenv shell $PYTHON`` would work, but ``pyenv init`` doesn't seem to
-    # modify the Bash environment. ??? So, I hand-set the variables instead.
-    export PYENV_VERSION=$PYTHON
-    export PATH="/Users/travis/.pyenv/shims:${PATH}"
-    pyenv-virtualenv venv
-    source venv/bin/activate
+  if [ ! -z "$CONDA" ]; then
+    if [ "$TRAVIS_OS_NAME" == "osx" ]; then
+      curl https://repo.continuum.io/miniconda/Miniconda3-latest-MacOSX-x86_64.sh --output miniconda.sh
+    fi
+    chmod +x miniconda.sh
+    ./miniconda.sh -b
+    export PATH=$HOME/miniconda3/bin:$PATH
+    conda update --yes conda
+    conda create --yes -n travis python=$CONDA
+    source activate travis
     # A manual check that the correct version of Python is running.
     python --version
   fi
diff --git a/requirements_dev.txt b/requirements_dev.txt
index 5fea1ed..ebdb195 100644
--- a/requirements_dev.txt
+++ b/requirements_dev.txt
@@ -1,12 +1,12 @@
 bump2version==0.5.10
-coverage==4.5.2
+coverage==4.5.3
 flake8==3.7.7
 mock==2.0.0
 pip==19.0.3
-pytest==4.3.0
+pytest==4.3.1
 pytest-runner==4.4
 six==1.12.0
-Sphinx==1.8.4
+Sphinx==1.8.5
 tox==3.7.0
 twine==1.13.0
 watchdog==0.9.0