diff --git a/.manylinux-install.sh b/.manylinux-install.sh
index 5762e5f..7dcf011 100755
--- a/.manylinux-install.sh
+++ b/.manylinux-install.sh
@@ -5,13 +5,12 @@ set -e -x
 # Compile wheels
 for PYBIN in /opt/python/*/bin; do
     if [[ "${PYBIN}" == *"cp27"* ]] || \
-       [[ "${PYBIN}" == *"cp33"* ]] || \
        [[ "${PYBIN}" == *"cp34"* ]] || \
        [[ "${PYBIN}" == *"cp35"* ]] || \
        [[ "${PYBIN}" == *"cp36"* ]]; then
         "${PYBIN}/pip" install -e /io/
         "${PYBIN}/pip" wheel /io/ -w wheelhouse/
-	rm -rf /io/build /io/*.egg-info	
+	rm -rf /io/build /io/*.egg-info
     fi
 done
 
@@ -19,4 +18,3 @@ done
 for whl in wheelhouse/BTrees*.whl; do
     auditwheel repair "$whl" -w /io/wheelhouse/
 done
-
diff --git a/.travis.yml b/.travis.yml
index 6925ae8..a4fdffb 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -7,14 +7,14 @@ matrix:
         - os: linux
           python: 2.7
           env: PURE_PYTHON=1
-        - os: linux
-          python: 3.3
         - os: linux
           python: 3.4
         - os: linux
           python: 3.5
         - os: linux
           python: 3.6
+        - os: linux
+          python: 3.7-dev
         - os: linux
           python: 3.6
           env: PURE_PYTHON=1
diff --git a/CHANGES.rst b/CHANGES.rst
index 0915694..748bc96 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,10 +1,11 @@
 ``BTrees`` Changelog
 ====================
 
-4.4.2 (unreleased)
+4.5.0 (unreleased)
 ------------------
 
-- Add support for Python 3.6.
+- Add support for Python 3.6 and 3.7.
+- Drop support for Python 3.3.
 - Raise an ``ImportError`` consistently on Python 3 if the C extension for
   BTrees is used but the ``persistent`` C extension is not available.
   Previously this could result in an odd ``AttributeError``. See
diff --git a/appveyor.yml b/appveyor.yml
index ac4216c..d37058c 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -7,8 +7,6 @@ environment:
   matrix:
     - python: 27
     - python: 27-x64
-    - python: 33
-    - python: 33-x64
     - python: 34
     - python: 34-x64
     - python: 35
diff --git a/setup.py b/setup.py
index a57891e..7136834 100644
--- a/setup.py
+++ b/setup.py
@@ -153,10 +153,10 @@ def BTreeExtension(family):
           'Programming Language :: Python :: 2',
           'Programming Language :: Python :: 2.7',
           'Programming Language :: Python :: 3',
-          'Programming Language :: Python :: 3.3',
           'Programming Language :: Python :: 3.4',
           'Programming Language :: Python :: 3.5',
           'Programming Language :: Python :: 3.6',
+          'Programming Language :: Python :: 3.7',
           "Programming Language :: Python :: Implementation :: CPython",
           "Programming Language :: Python :: Implementation :: PyPy",
           "Framework :: ZODB",
diff --git a/tox.ini b/tox.ini
index 16cf799..da99a31 100644
--- a/tox.ini
+++ b/tox.ini
@@ -3,7 +3,7 @@ envlist =
 # Jython support pending 2.7 support, due 2012-07-15 or so.  See:
 # http://fwierzbicki.blogspot.com/2012/03/adconion-to-fund-jython-27.html
 #   py27,jython,pypy,coverage,docs
-    py27,py27-pure,pypy,py33,py34,py35,py35-pure,py36,pypy3,w_zodb,coverage,docs
+    py27,py27-pure,pypy,py34,py35,py35-pure,py36,py37,pypy3,w_zodb,coverage,docs
 
 [testenv]
 usedevelop = true