diff --git a/.gitignore b/.gitignore
index d9a08dc..ebd257f 100644
--- a/.gitignore
+++ b/.gitignore
@@ -8,3 +8,4 @@
 /wheel-0.32.0.tar.gz
 /wheel-0.33.1.tar.gz
 /wheel-0.33.6.tar.gz
+/wheel-0.34.2.tar.gz
diff --git a/python-wheel.spec b/python-wheel.spec
index b4a4f78..ee0d7c2 100644
--- a/python-wheel.spec
+++ b/python-wheel.spec
@@ -13,8 +13,8 @@
 %global python_wheeldir %{_datadir}/python-wheels
 
 Name:           python-%{pypi_name}
-Version:        0.33.6
-Release:        6%{?dist}
+Version:        0.34.2
+Release:        1%{?dist}
 Epoch:          1
 Summary:        Built-package format for Python
 
@@ -23,46 +23,41 @@ URL:            https://github.com/pypa/wheel
 Source0:        %{url}/archive/%{version}/%{pypi_name}-%{version}.tar.gz
 BuildArch:      noarch
 
+BuildRequires:  python3-devel
+BuildRequires:  python3-setuptools
+
+# python3 bootstrap: this is rebuilt before the final build of python3, which
+# adds the dependency on python3-rpm-generators, so we require it manually
+BuildRequires:  python3-rpm-generators
+
 %if %{with tests}
+BuildRequires:  python3-pytest
 # several tests compile extensions
 # those tests are skipped if gcc is not found
 BuildRequires:  gcc
 %endif
 
-%{?python_enable_dependency_generator}
+%global _description %{expand:
+Wheel is the reference implementation of the Python wheel packaging standard,
+as defined in PEP 427.
 
-%global _description \
-A built-package format for Python.\
-\
-A wheel is a ZIP-format archive with a specially formatted filename and the\
-.whl extension. It is designed to contain all the files for a PEP 376\
-compatible install in a way that is very close to the on-disk format.
+It has two different roles:
+
+ 1. A setuptools extension for building wheels that provides the bdist_wheel
+    setuptools command.
+ 2. A command line tool for working with wheel files.}
 
 %description %{_description}
 
 
 %package -n     python3-%{pypi_name}
 Summary:        %{summary}
-BuildRequires:  python3-devel
-# python3 bootstrap: this is rebuilt before the final build of python3, which
-# adds the dependency on python3-rpm-generators, so we require it manually
-BuildRequires:  python3-rpm-generators
-BuildRequires:  python3-setuptools
-%if %{with tests}
-BuildRequires:  python3-pytest
-%endif
-%{?python_provide:%python_provide python3-%{pypi_name}}
-Conflicts:      python-%{pypi_name} < %{version}-%{release}
-
 %description -n python3-%{pypi_name} %{_description}
 
-Python 3 version.
-
 
 %if %{without bootstrap}
 %package wheel
 Summary:        The Python wheel module packaged as a wheel
-
 %description wheel
 A Python wheel of wheel to use with virtualenv.
 %endif
@@ -71,17 +66,10 @@ A Python wheel of wheel to use with virtualenv.
 %prep
 %autosetup -n %{pypi_name}-%{version} -p1
 
-# Empty files make rpmlint sad
-test -s wheel/cli/install.py || echo "# empty" > wheel/cli/install.py
-
 
 %build
 %py3_build
 
-%if %{without bootstrap}
-%py3_build_wheel
-%endif
-
 
 %install
 %py3_install
@@ -90,6 +78,9 @@ ln -s %{pypi_name}-%{python3_version} %{buildroot}%{_bindir}/%{pypi_name}-3
 ln -s %{pypi_name}-3 %{buildroot}%{_bindir}/%{pypi_name}
 
 %if %{without bootstrap}
+# We can only use bdist_wheel when wheel is installed, hence we don't build the wheel in %%build
+export PYTHONPATH=%{buildroot}%{python3_sitelib}
+%py3_build_wheel
 mkdir -p %{buildroot}%{python_wheeldir}
 install -p dist/%{python_wheelname} -t %{buildroot}%{python_wheeldir}
 %endif
@@ -97,17 +88,18 @@ install -p dist/%{python_wheelname} -t %{buildroot}%{python_wheeldir}
 
 %if %{with tests}
 %check
-rm setup.cfg
-PYTHONPATH=%{buildroot}%{python3_sitelib} py.test-3 -v --ignore build
+rm setup.cfg  # to drop pytest coverage options configured there
+%pytest -v --ignore build
 %endif
 
+
 %files -n python3-%{pypi_name}
 %license LICENSE.txt
 %doc README.rst
 %{_bindir}/%{pypi_name}
 %{_bindir}/%{pypi_name}-3
 %{_bindir}/%{pypi_name}-%{python3_version}
-%{python3_sitelib}/%{pypi_name}*
+%{python3_sitelib}/%{pypi_name}*/
 
 %if %{without bootstrap}
 %files wheel
@@ -118,6 +110,11 @@ PYTHONPATH=%{buildroot}%{python3_sitelib} py.test-3 -v --ignore build
 %endif
 
 %changelog
+* Mon Aug 10 2020 Miro Hrončok <mhroncok@redhat.com> - 1:0.34.2-1
+- Update to 0.34.2
+- Drops Python 3.4 support
+- Fixes: rhbz#1795134
+
 * Wed Jul 29 2020 Fedora Release Engineering <releng@fedoraproject.org> - 1:0.33.6-6
 - Rebuilt for https://fedoraproject.org/wiki/Fedora_33_Mass_Rebuild
 
diff --git a/sources b/sources
index f1e2f62..47cf987 100644
--- a/sources
+++ b/sources
@@ -1 +1 @@
-SHA512 (wheel-0.33.6.tar.gz) = 04edf619ee6fd06f1e4c8bc513c6e21ba91615eba42bca5473e60573e274133b1019774b8e3a960e05f5a69bb256508d0a8a31fd9ab91a28f1b87d1095b17b5e
+SHA512 (wheel-0.34.2.tar.gz) = fcd02cf770382c26b5250aa48f60481ac868ff7e1b08245ed4616aaa7d6dc5e3280d9ab787c4d1690b11550de9f6160c0d31dd65b79554711ab5d02de479e1ab
diff --git a/tests/tests.yml b/tests/tests.yml
index 4d7bc10..8ee0680 100644
--- a/tests/tests.yml
+++ b/tests/tests.yml
@@ -13,9 +13,6 @@
     - smoke27:
         dir: python/smoke
         run: VERSION=2.7 METHOD=virtualenv ./venv.sh
-    - smoke34_optional:
-        dir: python/smoke
-        run: VERSION=3.4 METHOD=virtualenv INSTALL_OR_SKIP=true ./venv.sh
     - smoke35:
         dir: python/smoke
         run: VERSION=3.5 METHOD=virtualenv ./venv.sh
@@ -37,7 +34,6 @@
     required_packages:
     - gcc
     - virtualenv
-    - python26
     - python27
     - python35
     - python36