diff --git a/python-flit.spec b/python-flit.spec
index f2122d5..9d84293 100644
--- a/python-flit.spec
+++ b/python-flit.spec
@@ -20,6 +20,7 @@ Source1:	https://pypi.org/pypi?%3Aaction=list_classifiers#/classifiers.lst
 
 BuildArch:	noarch
 BuildRequires:	python3-devel
+BuildRequires:	pyproject-rpm-macros
 BuildRequires:	python3-pip
 BuildRequires:	python3-requests
 BuildRequires:	python3-docutils
@@ -86,22 +87,17 @@ at flit_core.buildapi.
 export FLIT_NO_NETWORK=1
 
 # first, build flit_core with self
-# TODO do it in a less hacky way, this is reconstructed from pyoroject.toml
 cd flit_core
-PYTHONPATH=$PWD %{python3} -c 'from flit_core.build_thyself import build_wheel; build_wheel(".")'
-
-# %%py3_install_wheel unfortunately hardcodes installing from dist/
-mkdir ../dist
-mv flit_core-%{version}-py2.py3-none-any.whl ../dist
+%pyproject_wheel
+# Move %%{_pyproject_wheeldir}/flit_core wheel to the main dir
+mv %{_pyproject_wheeldir} ..
 cd -
 
-PYTHONPATH=$PWD:$PWD/flit_core %{python3} -m flit build --format wheel
-
+# build of the main flit (needs flit_core)
+PYTHONPATH=$PWD:$PWD/flit_core %pyproject_wheel
 
 %install
-%py3_install_wheel flit_core-%{version}-py2.py3-none-any.whl
-%py3_install_wheel flit-%{version}-py3-none-any.whl
-
+%pyproject_install
 
 %if %{with tests}
 %check