diff --git a/.gitignore b/.gitignore
index 45fb183..1a55827 100644
--- a/.gitignore
+++ b/.gitignore
@@ -18,3 +18,4 @@
 /flit-3.5.1.tar.gz
 /flit-3.7.1.tar.gz
 /flit-3.8.0.tar.gz
+/flit_core-3.8.0.tar.gz
diff --git a/python-flit-core.spec b/python-flit-core.spec
index eafd5d4..0620186 100644
--- a/python-flit-core.spec
+++ b/python-flit-core.spec
@@ -15,7 +15,7 @@ Summary:        PEP 517 build backend for packages using Flit
 License:        BSD-3-Clause
 
 URL:            https://flit.pypa.io/
-Source:         https://github.com/pypa/flit/archive/%{version}/flit-%{version}.tar.gz
+Source:         %{pypi_source flit_core}
 
 BuildArch:      noarch
 BuildRequires:  python3-devel
@@ -49,23 +49,21 @@ Requires:       python(abi) = %{python3_version}
 
 
 %prep
-%autosetup -p1 -n flit-%{version}
+%autosetup -p1 -n flit_core-%{version}
 
 # Remove vendored tomli that flit_core includes to solve the circular dependency on older Pythons
 # (flit_core requires tomli, but flit_core is needed to build tomli).
 # We don't use this, as tomllib is a part of standard library since Python 3.11.
-rm -rf flit_core/flit_core/vendor
+rm -rf flit_core/vendor
 
 
 %if %{without bootstrap}
 %generate_buildrequires
-cd flit_core
 %pyproject_buildrequires
 %endif
 
 
 %build
-cd flit_core
 %if %{with bootstrap}
 %{python3} -m flit_core.wheel
 %else
@@ -74,7 +72,6 @@ cd flit_core
 
 %install
 %if %{with bootstrap}
-cd flit_core
 %{python3} bootstrap_install.py --install-root %{buildroot} dist/flit_core-%{version}-py3-none-any.whl
 # for consistency with %%pyproject_install:
 rm %{buildroot}%{python3_sitelib}/flit_core-*.dist-info/RECORD
@@ -90,14 +87,15 @@ rm -r %{buildroot}%{python3_sitelib}/flit_core/tests/
 %check
 %py3_check_import flit_core flit_core.buildapi
 %if %{with tests}
-cd flit_core
 %pytest
 %endif
 
 
 %files -n python3-flit-core
 %license LICENSE
-%doc flit_core/README.rst
+# README.rst is missing from the sdist,
+# but it basically contains the %%description only,
+# so probably not worth adding anyway.
 %{python3_sitelib}/flit_core-*.dist-info/
 %{python3_sitelib}/flit_core/
 
diff --git a/sources b/sources
index 017d269..09ad911 100644
--- a/sources
+++ b/sources
@@ -1 +1 @@
-SHA512 (flit-3.8.0.tar.gz) = c4af79e1511e647303dc6b0913d8526586580db8d916aa7c4a52a9ebb281b375b6082e961ac8be05c0fc8ffdd8c3ec858fcba4e7faea25f465895288fa09c355
+SHA512 (flit_core-3.8.0.tar.gz) = 914804e3f2040762381afe039272d9d6fdbcd3f3cf8b9eea854f2f1d95edcb01718fd6685476bc1cdc251dfc46ef80b40f087df881d8b963dcc3f3332fd32a46