diff --git a/ostree-parse-pungi.py b/ostree-parse-pungi.py
index 45b8e035..6781d45b 100644
--- a/ostree-parse-pungi.py
+++ b/ostree-parse-pungi.py
@@ -44,5 +44,8 @@ for addtempvar in args["add_template_var"]:
 # this is where the previous step of the openQA test created the
 # ostree repo
 cmd = cmd.replace("https://kojipkgs.fedoraproject.org/compose/ostree/repo/", "file:///var/tmp/ostree/repo")
+# this changes to our custom ref name
+cmd = cmd.replace("ostree_install_ref=fedora/", "ostree_install_ref=fedora-openqa/")
+cmd = cmd.replace("ostree_update_ref=fedora/", "ostree_update_ref=fedora-openqa/")
 
 print(cmd)
diff --git a/tests/_ostree_build.pm b/tests/_ostree_build.pm
index 73ef6e54..f68e8e7d 100644
--- a/tests/_ostree_build.pm
+++ b/tests/_ostree_build.pm
@@ -46,6 +46,9 @@ sub run {
     my $repl = 'repos:\n  - advisory\n  - workarounds';
     $repl .= '\n  - koji-rawhide' if ($version eq $rawrel);
     assert_script_run 'sed -i -e "s,repos:,' . $repl . ',g" fedora-' . $lcsubv . '.yaml';
+    # change the ref name to a custom one (so we can test rebasing to
+    # the 'normal' ref later)
+    assert_script_run 'sed -i -e "s,ref: fedora/,ref: fedora-openqa/,g" fedora-' . $lcsubv . '.yaml';
     # upload the config so we can check it
     upload_logs "fedora-$lcsubv.yaml";
     assert_script_run 'popd';
@@ -74,7 +77,7 @@ sub run {
     assert_script_run 'git clone https://pagure.io/pungi-fedora.git';
     assert_script_run 'cd pungi-fedora/';
     assert_script_run "git checkout ${branch}";
-    assert_script_run 'wget https://pagure.io/fedora-qa/os-autoinst-distri-fedora/raw/main/f/ostree-parse-pungi.py', timeout => 120;
+    assert_script_run 'wget https://pagure.io/fedora-qa/os-autoinst-distri-fedora/raw/ostree-custom-ref/f/ostree-parse-pungi.py', timeout => 120;
     my $loraxargs = script_output "python3 ostree-parse-pungi.py $lcsubv $arch";
 
     # this 'temporary file cleanup' thing can actually wipe bits of
diff --git a/tests/rpmostree_rebase.pm b/tests/rpmostree_rebase.pm
index d3242a9e..2ecc6f0b 100644
--- a/tests/rpmostree_rebase.pm
+++ b/tests/rpmostree_rebase.pm
@@ -38,7 +38,12 @@ sub run {
         $rebase = $relnum - 1;
         # avoid rebasing from 37 to <37, bad stuff happens
         # FIXME when 38 branches, we should change this to RELNUM+1
-        $rebase = "rawhide" if ($relnum eq "37");
+        $rebase = "38" if ($relnum eq "37");
+        # on update tests, just rebase to the 'official' ref for the
+        # release, as opposed to the custom ref we used when building;
+        # this should be more reliable than a different release
+        $rebase = $relnum if (get_var("ADVISORY_OR_TASK"));
+        $rebase = "rawhide" if ($rebase eq get_var("RAWREL"));
         $target = "fedora/${rebase}/${arch}/silverblue";
     }
     elsif ($current =~ "coreos") {