diff --git a/python-coverage.spec b/python-coverage.spec
index 35b47c8..4c7fb2e 100644
--- a/python-coverage.spec
+++ b/python-coverage.spec
@@ -1,4 +1,4 @@
-%if 0%{?fedora}
+%if 0%{?fedora} || 0%{?rhel} >= 8
 %global with_python3 1
 %else
 %{!?python2_sitearch: %global python2_sitearch %(%{__python2} -c "from distutils.sysconfig import get_python_lib; print get_python_lib(1)")}
@@ -94,13 +94,6 @@ sed -i 's/\r//g' README.rst
 %if 0%{?with_python3}
 %py3_install
 mv %{buildroot}/%{_bindir}/coverage %{buildroot}/%{_bindir}/python3-coverage
-
-rm -rf coverage-3* coverage3
-
-for i in coverage3 coverage-%{?python3_shortver}; do
-  ln -s	python3-coverage $i
-done
-popd
 %endif # if with_python3
 
 %py2_install
@@ -115,6 +108,14 @@ for i in python2-coverage coverage coverage2 coverage-%{?python2_shortver}; do
   ln -s python-coverage $i
 done
 
+%if 0%{?with_python3}
+rm -rf coverage-3* coverage3
+
+for i in coverage3 coverage-%{?python3_shortver}; do
+  ln -s	python3-coverage $i
+done
+%endif # if with_python3
+popd
 
 %files -n python2-coverage
 %license LICENSE.txt NOTICE.txt