diff --git a/python-flit.spec b/python-flit.spec
index 68df314..fc02217 100644
--- a/python-flit.spec
+++ b/python-flit.spec
@@ -104,6 +104,11 @@ PYTHONPATH=$PWD:$PWD/flit_core %pyproject_wheel
 %install
 %pyproject_install
 
+# don't ship tests in flit_core package
+# if upstream decides to change the installation, it can be removed:
+# https://github.com/takluyver/flit/issues/403
+rm -r %{buildroot}%{python3_sitelib}/flit_core/tests/
+
 %if %{with tests}
 %check
 # flit attempts to download list of classifiers from PyPI, but not if it's cached
@@ -112,8 +117,7 @@ mkdir -p fake_cache/flit
 cp %{SOURCE1} fake_cache/flit
 export XDG_CACHE_HOME=$PWD/fake_cache
 
-export PYTHONPATH=%{buildroot}%{python3_sitelib}
-pytest-3
+%pytest
 %endif
 
 
@@ -136,6 +140,7 @@ pytest-3
 * Tue Mar 30 2021 Karolina Surma <ksurma@redhat.com> - 3.2.0-1
 - Update to 3.2.0
 Resolves: rhbz#1940399
+- Remove tests from the flip_core package
 
 * Wed Jan 27 2021 Fedora Release Engineering <releng@fedoraproject.org> - 3.0.0-3
 - Rebuilt for https://fedoraproject.org/wiki/Fedora_34_Mass_Rebuild