diff --git a/lib/utils.pm b/lib/utils.pm
index 32ed2193..cddd9bb0 100644
--- a/lib/utils.pm
+++ b/lib/utils.pm
@@ -697,7 +697,7 @@ sub _repo_setup_updates {
     disable_updates_repos(both => 0) if ($version > $currrel);
     # use the buildroot repo on Rawhide: see e.g.
     # https://pagure.io/fedora-ci/general/issue/376 for why
-    if (get_var("VERSION") eq get_var("RAWREL") && get_var("TEST") ne "support_server") {
+    if (get_var("VERSION") ge get_var("RAWREL") && get_var("TEST") ne "support_server") {
         assert_script_run 'printf "[koji-rawhide]\nname=koji-rawhide\nbaseurl=https://kojipkgs.fedoraproject.org/repos/rawhide/latest/' . $arch . '/\ncost=2000\nenabled=1\ngpgcheck=0\n" > /etc/yum.repos.d/koji-rawhide.repo';
     }
     if (get_var("CANNED")) {
diff --git a/tests/_container_build_kiwi.pm b/tests/_container_build_kiwi.pm
index fef4cba0..066f37dd 100644
--- a/tests/_container_build_kiwi.pm
+++ b/tests/_container_build_kiwi.pm
@@ -19,7 +19,7 @@ sub run {
     my $repoxml;
     my $releasever;
     my $mockver;
-    if ($version eq $rawrel) {
+    if ($version ge $rawrel) {
         $branch = "main";
         $repoxml = "repositories/core-rawhide.xml";
         $releasever = "Rawhide";
diff --git a/tests/_installer_build.pm b/tests/_installer_build.pm
index b1187715..94bea9b2 100644
--- a/tests/_installer_build.pm
+++ b/tests/_installer_build.pm
@@ -8,7 +8,7 @@ sub run {
     my $version = get_var("VERSION");
     my $currrel = get_var("CURRREL");
     my $rawrel = get_var("RAWREL");
-    my $repo = $version eq $rawrel ? "fedora-rawhide.repo" : "fedora.repo";
+    my $repo = $version ge $rawrel ? "fedora-rawhide.repo" : "fedora.repo";
     my $advortask = get_var("ADVISORY_OR_TASK");
     my $arch = get_var("ARCH");
     # python3-dnf is for updvercheck.py
@@ -27,7 +27,7 @@ sub run {
         $cmd .= " --isfinal --repo=/etc/yum.repos.d/fedora-updates.repo";
     }
     $cmd .= " --repo=/etc/yum.repos.d/workarounds.repo" if (get_workarounds);
-    $cmd .= " --repo=/etc/yum.repos.d/koji-rawhide.repo" if ($version eq $rawrel);
+    $cmd .= " --repo=/etc/yum.repos.d/koji-rawhide.repo" if ($version ge $rawrel);
     $cmd .= " --repo=/etc/yum.repos.d/advisory.repo" unless (get_var("TAG") || get_var("COPR"));
     $cmd .= " --repo=/etc/yum.repos.d/openqa-testtag.repo" if (get_var("TAG") || get_var("COPR"));
     $cmd .= " ./results";
diff --git a/tests/_live_build.pm b/tests/_live_build.pm
index f94a3e92..7038ee16 100644
--- a/tests/_live_build.pm
+++ b/tests/_live_build.pm
@@ -11,7 +11,7 @@ sub run {
     my $repoks;
     my $releasever;
     my $mockver;
-    if ($version eq $rawrel) {
+    if ($version ge $rawrel) {
         $branch = "main";
         $repoks = "fedora-repo-rawhide.ks";
         $releasever = "Rawhide";
@@ -56,7 +56,7 @@ sub run {
     # and the workaround repo
     $repos .= '\n[workarounds]\nname=Workarounds repo\nbaseurl=file:///mnt/workarounds_repo\nenabled=1\nmetadata_expire=3600\ngpgcheck=0\n' if ($workarounds);
     # also the buildroot repo, for Rawhide
-    if ($version eq $rawrel) {
+    if ($version ge $rawrel) {
         $repos .= '\n[koji-rawhide]\nname=Buildroot repo\nbaseurl=https://kojipkgs.fedoraproject.org/repos/f' . $version . '-build/latest/\$basearch/\nenabled=1\nmetadata_expire=3600\ngpgcheck=0\nskip_if_unavailable=1\n';
     }
     $repos .= '\"\"\"';
@@ -75,7 +75,7 @@ sub run {
     # and the workarounds repo
     assert_script_run 'echo "repo --name=workarounds --baseurl=file:///mnt/workarounds_repo" >> ' . $repoks if ($workarounds);
     # and the buildroot repo, for Rawhide
-    if ($version eq $rawrel) {
+    if ($version ge $rawrel) {
         assert_script_run 'echo "repo --name=koji-rawhide --baseurl=https://kojipkgs.fedoraproject.org/repos/f' . $version . '-build/latest/\$basearch/" >> ' . $repoks;
     }
     # now flatten the kickstart
diff --git a/tests/_ostree_build.pm b/tests/_ostree_build.pm
index 3266e6ae..db154d77 100644
--- a/tests/_ostree_build.pm
+++ b/tests/_ostree_build.pm
@@ -8,9 +8,9 @@ sub run {
     my $version = get_var("VERSION");
     my $currrel = get_var("CURRREL");
     my $rawrel = get_var("RAWREL");
-    my $repo = $version eq $rawrel ? "fedora-rawhide.repo" : "fedora.repo";
+    my $repo = $version ge $rawrel ? "fedora-rawhide.repo" : "fedora.repo";
     my $branch;
-    if ($version eq $rawrel) {
+    if ($version ge $rawrel) {
         $branch = "main";
     }
     else {
@@ -40,13 +40,13 @@ sub run {
     assert_script_run "git checkout ${branch}";
     # now copy the advisory, workaround repo and koji-rawhide config files
     assert_script_run 'cp /etc/yum.repos.d/workarounds.repo .' if ($workarounds);
-    assert_script_run 'cp /etc/yum.repos.d/koji-rawhide.repo .' if ($version eq $rawrel);
+    assert_script_run 'cp /etc/yum.repos.d/koji-rawhide.repo .' if ($version ge $rawrel);
     assert_script_run 'cp /etc/yum.repos.d/advisory.repo .' unless ($tag || $copr);
     assert_script_run 'cp /etc/yum.repos.d/openqa-testtag.repo .' if ($tag || $copr);
     # and add them to the config file
     my $repl = 'repos:';
     $repl .= '\n  - workarounds' if ($workarounds);
-    $repl .= '\n  - koji-rawhide' if ($version eq $rawrel);
+    $repl .= '\n  - koji-rawhide' if ($version ge $rawrel);
     $repl .= '\n  - advisory' unless ($tag || $copr);
     $repl .= '\n  - openqa-testtag' if ($tag || $copr);
     # Just add them to all config files, as the names change a lot
@@ -98,7 +98,7 @@ sub run {
         $cmd .= " --isfinal --repo=/etc/yum.repos.d/fedora-updates.repo";
     }
     $cmd .= " --repo=/etc/yum.repos.d/workarounds.repo" if ($workarounds);
-    $cmd .= " --repo=/etc/yum.repos.d/koji-rawhide.repo" if ($version eq $rawrel);
+    $cmd .= " --repo=/etc/yum.repos.d/koji-rawhide.repo" if ($version ge $rawrel);
     $cmd .= " --repo=/etc/yum.repos.d/advisory.repo" unless ($tag || $copr);
     $cmd .= " --repo=/etc/yum.repos.d/openqa-testtag.repo" if ($tag || $copr);
     $cmd .= " ./results";
diff --git a/tests/desktop_background.pm b/tests/desktop_background.pm
index 2e57329c..46d11b40 100644
--- a/tests/desktop_background.pm
+++ b/tests/desktop_background.pm
@@ -11,7 +11,7 @@ sub run {
     # don't have any requirement for what background Rawhide uses.
     my $version = get_var('VERSION');
     my $rawrel = get_var('RAWREL');
-    return unless ($version ne "Rawhide" && $version ne $rawrel);
+    return unless ($version ne "Rawhide" && $version lt $rawrel);
     # KDE shows a different version of the welcome center on major upgrades,
     # which breaks this test
     click_lastmatch if (get_var("DESKTOP") eq "kde" && get_var("ADVISORY_OR_TASK") && check_screen "kde_ok", 5);