diff --git a/.travis.yml b/.travis.yml
index 901dac8..4745dbf 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,9 +1,26 @@
 language: python
-python: 2.7
-env:
-  - TOX_ENV=py27
-  - TOX_ENV=pep8
-  - TOX_ENV=py34
+dist: xenial
+
+matrix:
+  include:
+     - python: 3.8
+       env:
+         - TOX_ENV=pep8
+     - python: 3.4
+       env:
+         - TOX_ENV=py34
+     - python: 3.5
+       env:
+         - TOX_ENV=py35
+     - python: 3.6
+       env:
+         - TOX_ENV=py36
+     - python: 3.7
+       env:
+         - TOX_ENV=py37
+     - python: 3.8
+       env:
+         - TOX_ENV=py38
 install:
   - pip install tox coveralls
 script:
diff --git a/setup.py b/setup.py
index 35a5b51..6c4b7f3 100644
--- a/setup.py
+++ b/setup.py
@@ -21,8 +21,8 @@ def read(fname):
     install_requires=[
         'six',
         'contexter',
-        'weakrefmethod',
     ],
+    python_requires='>=3.4',
     classifiers=[
         'Development Status :: 5 - Production/Stable',
         'Intended Audience :: Developers',
@@ -34,4 +34,3 @@ def read(fname):
         'Topic :: Software Development :: Libraries :: Python Modules',
     ],
 )
-
diff --git a/signalslot/slot.py b/signalslot/slot.py
index e7aab17..2ebb64f 100644
--- a/signalslot/slot.py
+++ b/signalslot/slot.py
@@ -4,15 +4,9 @@
 
 import types
 import weakref
-import sys
 
 from .signal import BaseSlot
-
-# We cannot test a branch for Python >= 3.4 in Python < 3.4.
-if sys.version_info < (3, 4):  # pragma: no cover
-    from weakrefmethod import WeakMethod
-else:  # pragma: no cover
-    from weakref import WeakMethod
+from weakref import WeakMethod
 
 
 class Slot(BaseSlot):
diff --git a/tox.ini b/tox.ini
index 61754be..d6f1e9e 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py27,pep8,py34
+envlist = pep8,py34,py35,py36,py37,py38
 
 [testenv]
 commands = py.test --doctest-modules signalslot