diff --git a/tox.ini b/tox.ini
index 6f7512bca..7a0d32c97 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,11 +1,22 @@
 [tox]
-envlist = py27, pypy, py33, py34, py35
+envlist = py27, pypy, py34, py35
 
 [testenv]
+basepython =
+    py27: {env:TOXPYTHON:python2.7}
+    pypy: {env:TOXPYTHON:pypy}
+    py34: {env:TOXPYTHON:python3.4}
+    py35: {env:TOXPYTHON:python3.5}
 deps =
     pytest
     -rrequirements.txt
+install_command =
+    python -m pip install -v {opts} {packages}
 commands =
+    # check that we have the expected Python version and architecture
+    python -c "import sys; print(sys.version)"
+    python -c "import struct; print(struct.calcsize('P') * 8)"
+    # run the test suite
     py.test
 
 [pytest]