diff --git a/bindep.txt b/bindep.txt
index a145f8b4..931e963d 100644
--- a/bindep.txt
+++ b/bindep.txt
@@ -10,17 +10,29 @@
 # will fall back to installing its default packages which
 # will potentially be detrimental to the tests executed.
 
-# OpenStack-CI's Jenkins needs curl
-# TODO(odyssey4me) remove this once https://review.openstack.org/288634 has merged
-# and the disk images are rebuilt and redeployed.
-curl
-wget
-
-# Requirements for Paramiko 2.0
+# Base requirements for Ubuntu
+build-essential   [platform:dpkg]
+git-core          [platform:dpkg]
 libssl-dev        [platform:dpkg]
 libffi-dev        [platform:dpkg]
+python2.7         [platform:dpkg]
+python-dev        [platform:dpkg]
+
+# Base requirements for CentOS
+gcc               [platform:rpm]
+gcc-c++           [platform:rpm]
+git               [platform:rpm]
+python-devel      [platform:rpm]
 libffi-devel      [platform:rpm]
 openssl-devel     [platform:rpm]
 
-# For selinux
+# For SELinux
 libselinux-python [platform:rpm]
+
+# For SSL SNI support
+python-pyasn1               [platform:dpkg]
+python-openssl              [platform:dpkg]
+python-ndg-httpsclient      [platform:ubuntu !platform:ubuntu-trusty]
+python2-pyasn1              [platform:rpm]
+pyOpenSSL                   [platform:rpm]
+python-ndg_httpsclient      [platform:rpm]
diff --git a/run_tests.sh b/run_tests.sh
index 40cb7ffe..0a49aa3e 100755
--- a/run_tests.sh
+++ b/run_tests.sh
@@ -17,23 +17,31 @@ set -euov
 
 FUNCTIONAL_TEST=${FUNCTIONAL_TEST:-true}
 
-# prep the host
-if [ "$(which apt-get)" ]; then
-  apt-get install -y build-essential python2.7 python-dev git-core libssl-dev libffi-dev
-fi
-
-if [ "$(which yum)" ]; then
-  yum install -y '@Development Tools' python-devel git libffi-devel openssl-devel
-fi
-
-# get pip, if necessary
+# Install pip
 if [ ! "$(which pip)" ]; then
   curl --silent --show-error --retry 5 \
     https://bootstrap.pypa.io/get-pip.py | sudo python2.7
 fi
 
-# install tox
-pip install tox
+# Install bindep and tox
+pip install bindep tox
+
+# CentOS 7 requires two additional packages:
+#   redhat-lsb-core - for bindep profile support
+#   epel-release    - required to install python-ndg_httpsclient/python2-pyasn1
+if [ "$(which yum)" ]; then
+    yum -y install redhat-lsb-core epel-release
+fi
+
+# Install OS packages using bindep
+if apt-get -v >/dev/null 2>&1 ; then
+    apt-get update
+    DEBIAN_FRONTEND=noninteractive \
+      apt-get -q --option "Dpkg::Options::=--force-confold" \
+      --assume-yes install `bindep -b -f bindep.txt test`
+else
+    yum install -y `bindep -b -f bindep.txt test`
+fi
 
 # run through each tox env and execute the test
 for tox_env in $(awk -F= '/envlist/ {print $2}' tox.ini | sed 's/,/ /g'); do