diff --git a/python-wheel.spec b/python-wheel.spec
index f835ffd..6c38837 100644
--- a/python-wheel.spec
+++ b/python-wheel.spec
@@ -26,17 +26,25 @@ Summary:        Built-package format for Python
 License:        MIT and (ASL 2.0 or BSD)
 URL:            https://github.com/pypa/wheel
 Source0:        %{url}/archive/%{version}/%{pypi_name}-%{version}.tar.gz
+# This is used in bootstrap mode where we manually install the wheel and
+# entrypoints
+Source1:        wheel-entrypoint
 BuildArch:      noarch
 
 BuildRequires:  python%{python3_pkgversion}-devel
-BuildRequires:  python%{python3_pkgversion}-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
 
+# Needed to manually build and unpack the wheel
+%if %{with bootstrap}
+BuildRequires:  python%{python3_pkgversion}-flit-core
+BuildRequires:  unzip
+%endif
+
 %if %{with tests}
 BuildRequires:  python%{python3_pkgversion}-pytest
+BuildRequires:  python%{python3_pkgversion}-setuptools
 # several tests compile extensions
 # those tests are skipped if gcc is not found
 BuildRequires:  gcc
@@ -69,44 +77,62 @@ Summary:        %{summary}
 %description -n python%{python3_pkgversion}-%{pypi_name} %{_description}
 
 
-%if %{without bootstrap}
 %package -n     %{python_wheel_pkg_prefix}-%{pypi_name}-wheel
 Summary:        The Python wheel module packaged as a wheel
 %{bundled}
 
 %description -n %{python_wheel_pkg_prefix}-%{pypi_name}-wheel
 A Python wheel of wheel to use with virtualenv.
-%endif
 
 
 %prep
 %autosetup -n %{pypi_name}-%{version} -p1
 
 
+%if %{without bootstrap}
+%generate_buildrequires
+%pyproject_buildrequires
+%endif
+
+
 %build
-%py3_build
+%if %{with bootstrap}
+%global _pyproject_wheeldir dist
+%python3 -m flit_core.wheel
+%else
+%pyproject_wheel
+%endif
 
 
 %install
-%py3_install
+# pip is not available when bootstrapping, so we need to unpack the wheel and
+# create the entrypoints manually.
+%if %{with bootstrap}
+mkdir -p %{buildroot}%{python3_sitelib}
+unzip %{_pyproject_wheeldir}/%{python_wheel_name} \
+    -d %{buildroot}%{python3_sitelib} -x wheel-%{version}.dist-info/RECORD
+install -Dpm 0755 %{SOURCE1} %{buildroot}%{_bindir}/wheel
+%py3_shebang_fix %{buildroot}%{_bindir}/wheel
+%else
+%pyproject_install
+%endif
+
 mv %{buildroot}%{_bindir}/%{pypi_name}{,-%{python3_version}}
 %if %{with main_python}
 ln -s %{pypi_name}-%{python3_version} %{buildroot}%{_bindir}/%{pypi_name}-3
 ln -s %{pypi_name}-3 %{buildroot}%{_bindir}/%{pypi_name}
 %endif
 
-%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_wheel_dir}
-install -p dist/%{python_wheel_name} -t %{buildroot}%{python_wheel_dir}
-%endif
+install -p %{_pyproject_wheeldir}/%{python_wheel_name} -t %{buildroot}%{python_wheel_dir}
 
 
+%check
+# Smoke test
+%{py3_test_envvars} wheel-%{python3_version} version
+%py3_check_import wheel
+
 %if %{with tests}
-%check
-rm setup.cfg  # to drop pytest coverage options configured there
 %pytest -v --ignore build
 %endif
 
@@ -120,13 +146,11 @@ rm setup.cfg  # to drop pytest coverage options configured there
 %endif
 %{python3_sitelib}/%{pypi_name}*/
 
-%if %{without bootstrap}
 %files -n %{python_wheel_pkg_prefix}-%{pypi_name}-wheel
 %license LICENSE.txt
 # we own the dir for simplicity
 %dir %{python_wheel_dir}/
 %{python_wheel_dir}/%{python_wheel_name}
-%endif
 
 %changelog
 * Tue Mar 14 2023 Maxwell G <maxwell@gtmx.me> - 1:0.40.0-1
diff --git a/wheel-entrypoint b/wheel-entrypoint
new file mode 100755
index 0000000..0f20b46
--- /dev/null
+++ b/wheel-entrypoint
@@ -0,0 +1,7 @@
+#!/usr/bin/python3
+import re
+import sys
+from wheel.cli import main
+if __name__ == "__main__":
+    sys.argv[0] = re.sub(r"(-script\.pyw|\.exe)?$", "", sys.argv[0])
+    sys.exit(main())