diff --git a/flit_core-3.6.0.tar.gz b/flit_core-3.6.0.tar.gz
deleted file mode 100644
index 115b69d..0000000
--- a/flit_core-3.6.0.tar.gz
+++ /dev/null
@@ -1,3 +0,0 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:5892962ab8b8ea945835b3a288fe9dd69316f1903d5288c3f5cafdcdd04756ad
-size 37534
diff --git a/flit_core-3.7.1.tar.gz b/flit_core-3.7.1.tar.gz
new file mode 100644
index 0000000..7aa1a73
--- /dev/null
+++ b/flit_core-3.7.1.tar.gz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:14955af340c43035dbfa96b5ee47407e377ee337f69e70f73064940d27d0a44f
+size 40330
diff --git a/python-flit-core.changes b/python-flit-core.changes
index fdb5538..a628792 100644
--- a/python-flit-core.changes
+++ b/python-flit-core.changes
@@ -1,3 +1,23 @@
+-------------------------------------------------------------------
+Fri Mar 25 12:10:11 UTC 2022 - Ben Greiner <code@bnavigator.de>
+
+- Update to version 3.7.1
+  * Support for external data files such as man pages or Jupyter
+    extension support files (PR #510).
+  * Project names are now lowercase in wheel filenames and
+    .dist-info folder names, in line with the specifications (PR
+    #498).
+  * Improved support for bootstrapping a Python environment, e.g.
+    for downstream packagers (PR #511). flit_core.wheel is usable
+    with python -m to create wheels before the build tool is
+    available, and flit_core sdists also include a script to
+    install itself from a wheel before installer is available.
+  * Use newer importlib APIs, fixing some deprecation warnings (PR
+    #499).
+  * Fix building packages which need execution to get the version
+    number, and have a relative import in __init__.py (PR #531).
+- Update bootstrapping process
+
 -------------------------------------------------------------------
 Sun Jan  9 14:53:21 UTC 2022 - Ben Greiner <code@bnavigator.de>
 
diff --git a/python-flit-core.spec b/python-flit-core.spec
index 221b25c..eddb46a 100644
--- a/python-flit-core.spec
+++ b/python-flit-core.spec
@@ -27,13 +27,12 @@
 %{?!python_module:%define python_module() python3-%{**}}
 %define skip_python2 1
 Name:           python-flit-core%{psuffix}
-Version:        3.6.0
+Version:        3.7.1
 Release:        0
 Summary:        Distribution-building parts of Flit
 License:        BSD-3-Clause
 URL:            https://github.com/pypa/flit
 Source0:        https://files.pythonhosted.org/packages/source/f/flit-core/flit_core-%{version}.tar.gz
-Source1:        https://github.com/pypa/flit/raw/%{version}/flit_core/build_dists.py
 BuildRequires:  %{python_module base >= 3.6}
 %if %{with test}
 BuildRequires:  %{python_module flit-core = %{version}}
@@ -52,22 +51,21 @@ Flit is a simple way to put Python packages and modules on PyPI.
 
 %prep
 %setup -q -n flit_core-%{version}
-cp %{SOURCE1} .
 
 %build
 # https://flit.readthedocs.io/en/latest/bootstrap.html
-python3 build_dists.py
+python3 -m flit_core.wheel
 
 %if !%{with test}
 %install
-%{python_expand # do manually what pip would do
+%{python_expand #
 mkdir -p %{buildroot}%{$python_sitelib}
-unzip dist/flit_core-%{version}-py3-none-any.whl -d %{buildroot}%{$python_sitelib}
-rm -r  %{buildroot}%{$python_sitelib}/flit_core/tests
-}
-%{python_expand # debundle after the bootstrap. See vendor/README
+$python bootstrap_install.py dist/flit_core-%{version}-py3-none-any.whl -i %{buildroot}%{$python_sitelib}
+# debundle after the bootstrap. See vendor/README
 sed -i 's/from .vendor import tomli/import tomli/'  %{buildroot}%{$python_sitelib}/flit_core/config.py
 rm -r %{buildroot}%{$python_sitelib}/flit_core/vendor
+# Don't package the tests
+rm -r  %{buildroot}%{$python_sitelib}/flit_core/tests
 }
 %{?python_compileall}
 %python_expand %fdupes %{buildroot}%{$python_sitelib}