diff --git a/python-setuptools_scm.spec b/python-setuptools_scm.spec
index f09044d..556eb48 100644
--- a/python-setuptools_scm.spec
+++ b/python-setuptools_scm.spec
@@ -23,7 +23,7 @@ BuildRequires:  mercurial
 BuildRequires:  python3dist(pytest)
 BuildRequires:  python3dist(setuptools) >= 45
 # virtualenv omitted, see https://github.com/pypa/setuptools_scm/pull/940
-# rich omitted, pulled in as build-backend dependency
+# rich omitted, pulled in only with the [rich] extra
 %endif
 
 %description
@@ -39,15 +39,26 @@ Setuptools_scm handles managing your Python package versions in SCM metadata.
 It also handles file finders for the supported SCMs.
 
 
-%pyproject_extras_subpkg -n python%{python3_pkgversion}-setuptools_scm toml
+# We don't package the [rich] extra on RHELs, to avoid pulling rich into the buildroot
+%pyproject_extras_subpkg -n python%{python3_pkgversion}-setuptools_scm toml%{!?rhel:,rich}
 
 
 %prep
 %autosetup -p1 -n setuptools-scm-%{version}
+# Upstream bogusly declares rich as a build-system dependency,
+# but the build works without it.
+# We remove it here to simplify the bootstrap loop
+# and to avoid the dependency in RHEL builds.
+# Upstream issue: https://github.com/pypa/setuptools_scm/issues/941
+# Upstream PR: https://github.com/pypa/setuptools_scm/pull/942
+# The PR does not apply cleanly to 8.0.3, so we sed it out instead.
+# The sed removes the first line with "rich" only:
+sed -i '0,/"rich"/{/"rich"/d}' pyproject.toml
+
 
 
 %generate_buildrequires
-%pyproject_buildrequires
+%pyproject_buildrequires %{?with_tests:%{!?rhel:-x rich}}
 
 
 %build