diff --git a/.travis.yml b/.travis.yml
index 4429cc0d5..fd2e8d172 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -5,8 +5,6 @@ group: edge
 
 matrix:
   include:
-    - os: linux
-      env: TESTENV=py34-cov
     - os: linux
       env: DOCKER=debian-jessie
       services: docker
@@ -30,7 +28,7 @@ matrix:
       env: TESTENV=py35-pyqt59
     - os: linux
       python: 3.6
-      env: TESTENV=py36-pyqt59
+      env: TESTENV=py36-pyqt59-cov
     - os: osx
       env: TESTENV=py36 OSX=elcapitan
       osx_image: xcode7.3
diff --git a/qutebrowser/browser/history.py b/qutebrowser/browser/history.py
index 2d5c263bc..c6624e157 100644
--- a/qutebrowser/browser/history.py
+++ b/qutebrowser/browser/history.py
@@ -173,9 +173,7 @@ class WebHistory(sql.SqlTable):
                       (hidden in completion)
             atime: Override the atime used to add the entry
         """
-        if not url.isValid():  # pragma: no cover
-            # the no cover pragma is a WORKAROUND for this not being covered in
-            # old Qt versions.
+        if not url.isValid():
             log.misc.warning("Ignoring invalid URL being added to history")
             return
 
@@ -320,6 +318,6 @@ def init(parent=None):
     history = WebHistory(parent=parent)
     objreg.register('web-history', history)
 
-    if objects.backend == usertypes.Backend.QtWebKit:
+    if objects.backend == usertypes.Backend.QtWebKit:  # pragma: no cover
         from qutebrowser.browser.webkit import webkithistory
         webkithistory.init(history)
diff --git a/qutebrowser/browser/webkit/certificateerror.py b/qutebrowser/browser/webkit/certificateerror.py
index d02ded76c..1d2df1562 100644
--- a/qutebrowser/browser/webkit/certificateerror.py
+++ b/qutebrowser/browser/webkit/certificateerror.py
@@ -41,7 +41,7 @@ class CertificateErrorWrapper(usertypes.AbstractCertificateErrorWrapper):
         try:
             # Qt >= 5.4
             return hash(self._error)
-        except TypeError:  # pragma: no cover
+        except TypeError:
             return hash((self._error.certificate().toDer(),
                          self._error.error()))
 
diff --git a/qutebrowser/mainwindow/statusbar/backforward.py b/qutebrowser/mainwindow/statusbar/backforward.py
index fe044e621..3a566e105 100644
--- a/qutebrowser/mainwindow/statusbar/backforward.py
+++ b/qutebrowser/mainwindow/statusbar/backforward.py
@@ -30,7 +30,6 @@ class Backforward(textbase.TextBase):
         """Called on URL changes."""
         tab = tabs.currentWidget()
         if tab is None:  # pragma: no cover
-            # WORKAROUND: Doesn't get tested on older PyQt
             self.setText('')
             self.hide()
             return
diff --git a/qutebrowser/misc/miscwidgets.py b/qutebrowser/misc/miscwidgets.py
index b4a17e638..94be76734 100644
--- a/qutebrowser/misc/miscwidgets.py
+++ b/qutebrowser/misc/miscwidgets.py
@@ -245,8 +245,7 @@ class WrapperLayout(QLayout):
     def sizeHint(self):
         return self._widget.sizeHint()
 
-    def itemAt(self, _index):  # pragma: no cover
-        # For some reason this sometimes gets called by Qt.
+    def itemAt(self, _index):
         return None
 
     def takeAt(self, _index):
diff --git a/qutebrowser/utils/urlutils.py b/qutebrowser/utils/urlutils.py
index 4cd0e94d0..71174b270 100644
--- a/qutebrowser/utils/urlutils.py
+++ b/qutebrowser/utils/urlutils.py
@@ -605,7 +605,7 @@ def safe_display_string(qurl):
         raise InvalidUrlError(qurl)
 
     host = qurl.host(QUrl.FullyEncoded)
-    if '..' in host:
+    if '..' in host:  # pragma: no cover
         # WORKAROUND for https://bugreports.qt.io/browse/QTBUG-60364
         return '(unparseable URL!) {}'.format(qurl.toDisplayString())
 
diff --git a/scripts/dev/check_coverage.py b/scripts/dev/check_coverage.py
index e22d3a155..14d3a9f49 100644
--- a/scripts/dev/check_coverage.py
+++ b/scripts/dev/check_coverage.py
@@ -53,8 +53,6 @@ PERFECT_FILES = [
         'browser/webkit/cookies.py'),
     ('tests/unit/browser/test_history.py',
         'browser/history.py'),
-    ('tests/unit/browser/test_history.py',
-        'browser/webkit/webkithistory.py'),
     ('tests/unit/browser/webkit/http/test_http.py',
         'browser/webkit/http.py'),
     ('tests/unit/browser/webkit/http/test_content_disposition.py',
@@ -73,7 +71,7 @@ PERFECT_FILES = [
     ('tests/unit/browser/test_signalfilter.py',
         'browser/signalfilter.py'),
     (None,
-        'browser/webkit/certificateerror.py'),
+        'browser/webengine/certificateerror.py'),
     # ('tests/unit/browser/test_tab.py',
     #     'browser/tab.py'),
 
@@ -272,8 +270,8 @@ def main_check():
         subprocess.check_call([sys.executable, '-m', 'coverage', 'report',
                                '--show-missing', '--include', filters])
         print()
-        print("To debug this, run 'tox -e py35-cov' (or py34-cov) locally and "
-              "check htmlcov/index.html")
+        print("To debug this, run 'tox -e py36-pyqt59-cov' "
+              "(or py35-pyqt59-cov) locally and check htmlcov/index.html")
         print("or check https://codecov.io/github/qutebrowser/qutebrowser")
         print()
 
diff --git a/scripts/dev/ci/travis_install.sh b/scripts/dev/ci/travis_install.sh
index dd9d47640..62314b2b1 100644
--- a/scripts/dev/ci/travis_install.sh
+++ b/scripts/dev/ci/travis_install.sh
@@ -118,11 +118,6 @@ pip --version
 tox --version
 
 case $TESTENV in
-    py34-cov)
-        pip_install -r misc/requirements/requirements-codecov.txt
-        apt_install xvfb $pyqt_pkgs libpython3.4-dev gdb apport libqt5webkit5-dbg python3-pyqt5-dbg python3-pyqt5.qtquick-dbg python3-pyqt5.qtwebkit-dbg python3-dbg
-        check_pyqt
-        ;;
     py3*-pyqt*)
         #apt_install xvfb geoclue gdb apport
         ;;
diff --git a/tests/unit/utils/usertypes/test_question.py b/tests/unit/utils/usertypes/test_question.py
index 031e304cc..b11c01b6a 100644
--- a/tests/unit/utils/usertypes/test_question.py
+++ b/tests/unit/utils/usertypes/test_question.py
@@ -89,3 +89,12 @@ def test_abort_typeerror(question, qtbot, mocker, caplog):
     with caplog.at_level(logging.ERROR, 'misc'):
         question.abort()
     assert caplog.records[0].message == 'Error while aborting question'
+
+
+def test_abort_twice(question, qtbot):
+    """Abort a question twice."""
+    with qtbot.wait_signal(question.aborted):
+        question.abort()
+    assert question.is_aborted
+    with qtbot.assert_not_emitted(question.aborted):
+        question.abort()
diff --git a/tox.ini b/tox.ini
index 04cf826d1..e916f4a83 100644
--- a/tox.ini
+++ b/tox.ini
@@ -4,7 +4,7 @@
 # and then run "tox" from this directory.
 
 [tox]
-envlist = py36-cov,misc,vulture,flake8,pylint,pyroma,check-manifest,eslint
+envlist = py36-pyqt59-cov,misc,vulture,flake8,pylint,pyroma,check-manifest,eslint
 distshare = {toxworkdir}
 skipsdist = true
 
@@ -21,39 +21,6 @@ commands =
     {envpython} scripts/link_pyqt.py --tox {envdir}
     {envpython} -bb -m pytest {posargs:tests}
 
-
-# test envs with coverage
-
-[testenv:py36-cov]
-basepython = python3.6
-setenv = {[testenv]setenv}
-passenv = {[testenv]passenv}
-deps = {[testenv]deps}
-commands =
-    {envpython} scripts/link_pyqt.py --tox {envdir}
-    {envpython} -bb -m pytest --cov --cov-report xml --cov-report=html --cov-report= {posargs:tests}
-    {envpython} scripts/dev/check_coverage.py {posargs}
-
-[testenv:py35-cov]
-basepython = python3.5
-setenv = {[testenv]setenv}
-passenv = {[testenv]passenv}
-deps = {[testenv]deps}
-commands =
-    {envpython} scripts/link_pyqt.py --tox {envdir}
-    {envpython} -bb -m pytest --cov --cov-report xml --cov-report=html --cov-report= {posargs:tests}
-    {envpython} scripts/dev/check_coverage.py {posargs}
-
-[testenv:py34-cov]
-basepython = python3.4
-setenv = {[testenv]setenv}
-passenv = {[testenv]passenv}
-deps = {[testenv]deps}
-commands =
-    {envpython} scripts/link_pyqt.py --tox {envdir}
-    {envpython} -bb -m pytest --cov --cov-report xml --cov-report=html --cov-report= {posargs:tests}
-    {envpython} scripts/dev/check_coverage.py {posargs}
-
 # test envs with PyQt5 from PyPI
 
 [testenv:py35-pyqt56]
@@ -133,6 +100,34 @@ deps =
     PyQt5==5.9
 commands = {envpython} -bb -m pytest {posargs:tests}
 
+# test envs with coverage
+
+[testenv:py35-pyqt59-cov]
+basepython = python3.6
+setenv =
+    {[testenv]setenv}
+    QUTE_BDD_WEBENGINE=true
+passenv = {[testenv]passenv}
+deps =
+    {[testenv]deps}
+    PyQt5==5.9
+commands =
+    {envpython} -bb -m pytest --cov --cov-report xml --cov-report=html --cov-report= {posargs:tests}
+    {envpython} scripts/dev/check_coverage.py {posargs}
+
+[testenv:py36-pyqt59-cov]
+basepython = python3.5
+setenv =
+    {[testenv]setenv}
+    QUTE_BDD_WEBENGINE=true
+passenv = {[testenv]passenv}
+deps =
+    {[testenv]deps}
+    PyQt5==5.9
+commands =
+    {envpython} -bb -m pytest --cov --cov-report xml --cov-report=html --cov-report= {posargs:tests}
+    {envpython} scripts/dev/check_coverage.py {posargs}
+
 # other envs
 
 [testenv:mkvenv]