diff --git a/python-wheel.spec b/python-wheel.spec
index f712a78..b8a0001 100644
--- a/python-wheel.spec
+++ b/python-wheel.spec
@@ -14,12 +14,11 @@
 %bcond_without main_python
 
 %global pypi_name wheel
-%global python_wheelname %{pypi_name}-%{version}-py2.py3-none-any.whl
-%global python_wheeldir %{_datadir}/python-wheels
+%global python_wheel_name %{pypi_name}-%{version}-py2.py3-none-any.whl
 
 Name:           python-%{pypi_name}
 Version:        0.36.2
-Release:        4%{?dist}
+Release:        5%{?dist}
 Epoch:          1
 Summary:        Built-package format for Python
 
@@ -71,11 +70,13 @@ Summary:        %{summary}
 
 
 %if %{without bootstrap}
-%package wheel
+%package -n     %{python_wheel_pkg_prefix}-%{pypi_name}-wheel
 Summary:        The Python wheel module packaged as a wheel
 %{bundled}
+Provides:       %{name}-wheel = %{epoch}:%{version}-%{release}
+Obsoletes:      %{name}-wheel < %{epoch}:%{version}-%{release}
 
-%description wheel
+%description -n %{python_wheel_pkg_prefix}-%{pypi_name}-wheel
 A Python wheel of wheel to use with virtualenv.
 %endif
 
@@ -100,8 +101,8 @@ ln -s %{pypi_name}-3 %{buildroot}%{_bindir}/%{pypi_name}
 # 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}
+mkdir -p %{buildroot}%{python_wheel_dir}
+install -p dist/%{python_wheel_name} -t %{buildroot}%{python_wheel_dir}
 %endif
 
 
@@ -122,14 +123,19 @@ rm setup.cfg  # to drop pytest coverage options configured there
 %{python3_sitelib}/%{pypi_name}*/
 
 %if %{without bootstrap}
-%files wheel
+%files -n %{python_wheel_pkg_prefix}-%{pypi_name}-wheel
 %license LICENSE.txt
 # we own the dir for simplicity
-%dir %{python_wheeldir}/
-%{python_wheeldir}/%{python_wheelname}
+%dir %{python_wheel_dir}/
+%{python_wheel_dir}/%{python_wheel_name}
 %endif
 
 %changelog
+* Wed Sep 22 2021 Tomas Orsava <torsava@redhat.com> - 1:0.36.2-5
+- Make the python-wheel-wheel subpackage versioned (python3-wheel-wheel),
+  and move its contents to a versioned directory /usr/share/python3-wheels
+- Resolves: rhbz#1982668
+
 * Tue Aug 10 2021 Mohan Boddu <mboddu@redhat.com> - 1:0.36.2-4
 - Rebuilt for IMA sigs, glibc 2.34, aarch64 flags
   Related: rhbz#1991688