diff --git a/.travis.yml b/.travis.yml
index 2392754..8fc5429 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,12 +1,9 @@
 language: python
 dist: xenial
 python:
-  - 2.7
-  - 3.5
   - 3.6
   - 3.7
   - 3.8
-  - pypy
   - pypy3
 install:
   - pip install tox-travis coveralls
diff --git a/CHANGES.rst b/CHANGES.rst
index 9acc96b..02d12e3 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -2,10 +2,18 @@
 Change log for gocept.pytestlayer
 =================================
 
-6.4 (unreleased)
+7.0 (unreleased)
 ================
 
-- Nothing changed yet.
+Backwards imcompatible changes
+------------------------------
+
+- Drop support for Python 2.7 and 3.5 and ``pytest < 5.0``. (#8)
+
+Features
+--------
+
+- Support ``pytest >= 6.0``. (#8)
 
 
 6.3 (2020-05-15)
diff --git a/README.rst b/README.rst
index 49a9e49..1616cc8 100644
--- a/README.rst
+++ b/README.rst
@@ -18,9 +18,8 @@ The gocept.pytestlayer distribution
 Integration of zope.testrunner-style test layers into the `py.test`_
 framework
 
-This package is compatible with Python versions 2.7 and 3.5 - 3.8 including
-PyPy implementation. (To run its tests successfully you should use at least
-Python 2.7.4 because of a bug in earlier Python 2.7 versions.)
+This package is compatible with Python versions 3.6 - 3.8 including
+PyPy3.
 
 .. _`py.test` : http://pytest.org
 
diff --git a/setup.py b/setup.py
index 684185b..45abc8d 100644
--- a/setup.py
+++ b/setup.py
@@ -5,20 +5,14 @@
 
 setup(
     name='gocept.pytestlayer',
-    version='6.4.dev0',
+    version='7.0.dev0',
 
     python_requires=', '.join([
-        '>=2.7',
-        '!=3.0.*',
-        '!=3.1.*',
-        '!=3.2.*',
-        '!=3.3.*',
-        '!=3.4.*',
+        '>=3.6',
     ]),
     install_requires=[
         'pytest',
         'setuptools',
-        'six',
         'zope.dottedname',
     ],
 
@@ -55,10 +49,7 @@
 Natural Language :: English
 Operating System :: OS Independent
 Programming Language :: Python
-Programming Language :: Python :: 2
-Programming Language :: Python :: 2.7
 Programming Language :: Python :: 3
-Programming Language :: Python :: 3.5
 Programming Language :: Python :: 3.6
 Programming Language :: Python :: 3.7
 Programming Language :: Python :: 3.8
diff --git a/src/gocept/pytestlayer/_compat.py b/src/gocept/pytestlayer/_compat.py
index ab69589..b0cb2a9 100644
--- a/src/gocept/pytestlayer/_compat.py
+++ b/src/gocept/pytestlayer/_compat.py
@@ -1,23 +1,17 @@
-import six
+# copied from Python 2.7 source code as plone testing uses __bases__
+def _searchbases(cls, accum):
+    # Simulate the "classic class" search order.
+    if cls in accum:
+        return
+    accum.append(cls)
+    for base in cls.__bases__:
+        _searchbases(base, accum)
 
-
-if six.PY2:
-    from inspect import getmro
-else:
-    # copied from Python 2.7 source code as plone testing uses __bases__
-    def _searchbases(cls, accum):
-        # Simulate the "classic class" search order.
-        if cls in accum:
-            return
-        accum.append(cls)
-        for base in cls.__bases__:
-            _searchbases(base, accum)
-
-    def getmro(cls):
-        "Return tuple of base classes in method resolution order."
-        if hasattr(cls, "__mro__"):
-            return cls.__mro__
-        else:
-            result = []
-            _searchbases(cls, result)
-            return tuple(result)
+def getmro(cls):
+    "Return tuple of base classes in method resolution order."
+    if hasattr(cls, "__mro__"):
+        return cls.__mro__
+    else:
+        result = []
+        _searchbases(cls, result)
+        return tuple(result)
diff --git a/src/gocept/pytestlayer/fixture.py b/src/gocept/pytestlayer/fixture.py
index 920ae1b..79bc454 100644
--- a/src/gocept/pytestlayer/fixture.py
+++ b/src/gocept/pytestlayer/fixture.py
@@ -2,7 +2,6 @@
 import imp
 import pytest
 import re
-import six
 import time
 import zope.dottedname.resolve
 
@@ -26,7 +25,7 @@ def timer(request, text):
     yield
     if verbose:
         time_taken = time.time() - start
-        reporter.write("{0:.3f}".format(time_taken), green=1, bold=1)
+        reporter.write(f"{time_taken:.3f}", green=1, bold=1)
         reporter.write_line(" seconds.")
 
 
@@ -36,7 +35,7 @@ def setup_layer(layer, request):
     layer_name = get_layer_name(layer)
     if hasattr(layer, 'setUp'):
         print(layer_name)
-        with timer(request, "Set up {0} in ".format(layer_name)):
+        with timer(request, f"Set up {layer_name} in "):
             layer.setUp()
         state.current.add(layer)
 
@@ -46,7 +45,7 @@ def teardown_layer(layer, request):
     state = request.session.zopelayer_state
     layer_name = get_layer_name(layer)
     if hasattr(layer, 'tearDown'):
-        with timer(request, "Tear down {0} in ".format(layer_name)):
+        with timer(request, f"Tear down {layer_name} in "):
             layer.tearDown()
         state.current.remove(layer)
 
@@ -137,7 +136,7 @@ def create(*layers, **kw):
 
     ns = {}
     for layer in layers:
-        if isinstance(layer, six.string_types):
+        if isinstance(layer, str):
             layer = zope.dottedname.resolve.resolve(layer)
         ns.update(_create_single(layer, **kw))
     return ns
@@ -215,9 +214,9 @@ def raise_if_bad_layer(layer):
 
     if not hasattr(layer, '__bases__'):
         raise RuntimeError(
-            "The layer {0} has no __bases__ attribute."
+            "The layer {layer!r} has no __bases__ attribute."
             " Layers may be of two sorts: class or instance with __bases__"
-            " attribute.".format(repr(layer))
+            " attribute."
         )
 
 
diff --git a/src/gocept/pytestlayer/layered.py b/src/gocept/pytestlayer/layered.py
index 9f1808c..acd976f 100644
--- a/src/gocept/pytestlayer/layered.py
+++ b/src/gocept/pytestlayer/layered.py
@@ -10,22 +10,26 @@ def collect(self):
         suite = self.obj()
         for item, layer in walk_suite(suite):
             fixture.parsefactories(self.parent, layer)
-            yield LayeredTestCaseInstance(item, self, layer)
+            yield LayeredTestCaseInstance.from_parent(
+                parent=self, obj=item, layer=layer)
 
 
 class LayeredTestCaseInstance(pytest.Collector):
 
-    def __init__(self, obj, parent, layer):
+    @classmethod
+    def from_parent(cls, parent, obj, layer, **kw):
         testname = repr(obj)  # fantastic doctest API :(
-        super(pytest.Collector, self).__init__(testname, parent=parent)
+        instance = super(pytest.Collector, cls).from_parent(
+            parent=parent, name=testname)
         # store testcase instance and layer
         # to pass them to function
-        self.obj = obj
-        self.layer = layer
-        self.extra_keyword_matches.update(fixture.get_keywords(layer))
+        instance.obj = obj
+        instance.layer = layer
+        instance.extra_keyword_matches.update(fixture.get_keywords(layer))
+        return instance
 
     def collect(self):
-        yield LayeredTestCaseFunction('runTest', parent=self)
+        yield LayeredTestCaseFunction.from_parent(parent=self, name='runTest')
 
     def reportinfo(self):
         pass
@@ -33,16 +37,19 @@ def reportinfo(self):
 
 class LayeredTestCaseFunction(_pytest.unittest.TestCaseFunction):
 
-    def __init__(self, name, parent):
+    @classmethod
+    def from_parent(cls, parent, name, **kw):
         description = get_description(parent)
         keywords = get_keywords(description)
-        super(LayeredTestCaseFunction, self).__init__(
-            name, parent=parent,
-            keywords=keywords
+        function = super(LayeredTestCaseFunction, cls).from_parent(
+            parent=parent,
+            name=name,
+            keywords=keywords,
         )
-        self.layer = self.parent.layer
-        self.tc_description = description
-        self._testcase = self.parent.obj
+        function.layer = function.parent.layer
+        function.tc_description = description
+        function._testcase = function.parent.obj
+        return function
 
     def setup(self):
         # This is actually set in the base class, but as we want to modify
diff --git a/src/gocept/pytestlayer/plugin.py b/src/gocept/pytestlayer/plugin.py
index 0e67951..83dc867 100644
--- a/src/gocept/pytestlayer/plugin.py
+++ b/src/gocept/pytestlayer/plugin.py
@@ -16,7 +16,8 @@ def pytest_pycollect_makeitem(collector, name, obj):
 
     suite = query_testsuite(obj)
     if suite is not None:
-        return layered.LayeredTestSuite(name, parent=collector)
+        return layered.LayeredTestSuite.from_parent(
+            parent=collector, name=name)
     else:
         layer = query_layer(obj)
         if layer is not None:
diff --git a/tox.ini b/tox.ini
index 6e6818f..12c328a 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,13 +1,10 @@
 [tox]
 minversion = 2.4
 envlist =
-    py27,
-    py35,
-    py36,
-    py37,
-    py38,
-    pypy,
-    pypy3,
+    py36
+    py37
+    py38
+    pypy3
     coverage-report
 
 [testenv]
@@ -18,11 +15,10 @@ setenv =
   COVERAGE_FILE=.coverage.{envname}
 extras = test
 deps =
-    py{27,py}: pytest < 5.0
-    py{35,36,37,38,py3}: pytest >= 5.4.2
+    pytest >= 5.4.2
     pytest-cov
     pytest-flake8
-    py{35,36,37,38,py3}: pytest-remove-stale-bytecode
+    pytest-remove-stale-bytecode
 
 [testenv:coverage-report]
 deps = coverage