diff --git a/python-wheel.spec b/python-wheel.spec
index 022853f..566f18d 100644
--- a/python-wheel.spec
+++ b/python-wheel.spec
@@ -1,20 +1,16 @@
-# Note that the only function of bootstrap is that it disables the test suite:
-#   bcond_with bootstrap = tests enabled
+# Note that the function of bootstrap is that it disables the test suite and whl
+#   bcond_with bootstrap = tests enabled, package with whl created
 %bcond_with bootstrap
 
 %bcond_without python2
-%if 0%{?rhel} && 0%{?rhel} <= 7 && 0%{!?epel:1}
-# Note(hguemar): EL7 has no python3 stack but EPEL does
-%bcond_with python3
-%else
-%bcond_without python3
-%endif
 
 %global pypi_name wheel
+%global python_wheelname %{pypi_name}-%{version}-py2.py3-none-any.whl
+%global python_wheeldir %{_datadir}/python-wheels
 
 Name:           python-%{pypi_name}
 Version:        0.31.1
-Release:        2%{?dist}
+Release:        3%{?dist}
 Epoch:          1
 Summary:        Built-package format for Python
 
@@ -59,12 +55,11 @@ Python 2 version.
 %endif
 
 
-%if %{with python3}
 %package -n     python3-%{pypi_name}
 Summary:        %{summary}
 BuildRequires:  python3-devel
 BuildRequires:  python3-setuptools
-%if ! %{with bootstrap}
+%if %{without bootstrap}
 BuildRequires:  python3-pytest
 BuildRequires:  python3-pyxdg
 BuildRequires:  python3-keyring
@@ -74,6 +69,14 @@ BuildRequires:  python3-keyring
 %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
 
 
@@ -87,17 +90,17 @@ sed -ie '1d' %{pypi_name}/{egg2wheel,wininst2wheel}.py
 %if %{with python2}
 %py2_build
 %endif
-%if %{with python3}
 %py3_build
+
+%if %{without bootstrap}
+%py3_build_wheel
 %endif
 
 
 %install
-%if %{with python3}
 %py3_install
 mv %{buildroot}%{_bindir}/%{pypi_name}{,-%{python3_version}}
 ln -s %{pypi_name}-%{python3_version} %{buildroot}%{_bindir}/%{pypi_name}-3
-%endif
 
 %if %{with python2}
 %py2_install
@@ -106,17 +109,19 @@ ln -s %{pypi_name}-%{python2_version} %{buildroot}%{_bindir}/%{pypi_name}-2
 ln -s %{pypi_name}-2 %{buildroot}%{_bindir}/%{pypi_name}
 %endif
 
-%if ! %{with bootstrap}
+%if %{without bootstrap}
+mkdir -p %{buildroot}%{python_wheeldir}
+install -p dist/%{python_wheelname} -t %{buildroot}%{python_wheeldir}
+
+
 %check
 export LC_ALL=C.UTF-8
 rm setup.cfg
 %if %{with python2}
 PYTHONPATH=%{buildroot}%{python2_sitelib} py.test-2 -v --ignore build
 %endif
-%if %{with python3}
 PYTHONPATH=%{buildroot}%{python3_sitelib} py.test-3 -v --ignore build
 %endif
-%endif
 
 %if %{with python2}
 %files -n python2-%{pypi_name}
@@ -128,16 +133,25 @@ PYTHONPATH=%{buildroot}%{python3_sitelib} py.test-3 -v --ignore build
 %{python2_sitelib}/%{pypi_name}*
 %endif
 
-%if %{with python3}
 %files -n python3-%{pypi_name}
 %license LICENSE.txt
 %doc CHANGES.txt README.rst
 %{_bindir}/%{pypi_name}-3
 %{_bindir}/%{pypi_name}-%{python3_version}
 %{python3_sitelib}/%{pypi_name}*
+
+%if %{without bootstrap}
+%files wheel
+%license LICENSE.txt
+# we own the dir for simplicity
+%dir %{python_wheeldir}/
+%{python_wheeldir}/%{python_wheelname}
 %endif
 
 %changelog
+* Wed Aug 15 2018 Miro Hrončok <mhroncok@redhat.com> - 1:0.31.1-3
+- Create python-wheel-wheel package with the wheel of wheel
+
 * Sat Jul 14 2018 Fedora Release Engineering <releng@fedoraproject.org> - 1:0.31.1-2
 - Rebuilt for https://fedoraproject.org/wiki/Fedora_29_Mass_Rebuild