diff --git a/.coveragerc b/.coveragerc
index 5684cf9..af7e56f 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -1,6 +1,6 @@
 [run]
 source = $COVERAGE_HOME/src/zdaemon
-omit = */tests/*, */__main__.py
+omit = */__main__.py
 parallel = true
 data_file = $COVERAGE_HOME/.coverage
 
diff --git a/.travis.yml b/.travis.yml
index cff6a88..4f6e73d 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,16 +2,28 @@ language: python
 sudo: false
 python:
     - 2.7
-    - 3.3
     - 3.4
     - 3.5
+    - 3.6
     - pypy
-#   PyPy3 support pending a release of a fix for
-#   https://bitbucket.org/pypy/pypy/issue/1946)
-#   - pypy3
+    - pypy3
+matrix:
+    include:
+        - python: "3.7"
+          dist: xenial
+          sudo: true
 install:
-    - pip install .
+    - pip install -U pip setuptools
+    - pip install -U coverage coveralls
+    - pip install -U -e .[test]
 script:
-    - python setup.py -q test -q
+    - export COVERAGE_HOME=$(pwd)
+    - export COVERAGE_PROCESS_START=$COVERAGE_HOME/.coveragerc
+    - coverage run -m zope.testrunner --test-path=src
+    - coverage combine
+after_success:
+    - coveralls
 notifications:
     email: false
+cache: pip
+
diff --git a/CHANGES.rst b/CHANGES.rst
index f347075..6e301c9 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -2,10 +2,12 @@
 Change log
 ==========
 
-4.2.1 (unreleased)
+4.3.0 (unreleased)
 ==================
 
-- Nothing changed yet.
+- Add support for Python 3.6 and 3.7.
+
+- Drop support for Python 3.3.
 
 
 4.2.0 (2016-12-07)
diff --git a/setup.py b/setup.py
index 13e8ee6..53c958f 100644
--- a/setup.py
+++ b/setup.py
@@ -57,7 +57,7 @@ def alltests():
 
 setup(
     name="zdaemon",
-    version='4.2.1.dev0',
+    version='4.3.0.dev0',
     url="https://github.com/zopefoundation/zdaemon",
     license="ZPL 2.1",
     description=
@@ -81,9 +81,10 @@ def alltests():
        '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',
        'Operating System :: POSIX',
diff --git a/tox.ini b/tox.ini
index 1b33771..e055ace 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,31 +1,23 @@
 [tox]
-#   PyPy3 support pending a release of a fix for
-#   https://bitbucket.org/pypy/pypy/issue/1946)
-#envlist = py27,py33,py34,pypy,pypy3
-envlist = py27,py33,py34,py35,pypy
+envlist = py27,py34,py35,py36,py37,pypy,pypy3,coverage
 
 [testenv]
 commands =
-    python setup.py -q test -q
-# without explicit deps, setup.py test will download a bunch of eggs into $PWD
+    zope-testrunner --test-path=src []
 deps =
-    zc.customdoctests
-    zope.testing
-    zope.testrunner
-    manuel
-    mock
+    .[test]
 
 [testenv:coverage]
 usedevelop = true
 basepython =
-    python2.7
+    python3.6
 setenv =
     COVERAGE_HOME={toxinidir}
     COVERAGE_PROCESS_START={toxinidir}/.coveragerc
 commands =
-    coverage run --source=zdaemon setup.py -q test
+    coverage run -m zope.testrunner --test-path=src []
     coverage combine
-    coverage report
+    coverage report --fail-under=83
 deps =
     {[testenv]deps}
     coverage