diff --git a/tests/kolainst/destructive/apply-live b/tests/kolainst/destructive/apply-live
index f9d87160e0..25310aeca4 100755
--- a/tests/kolainst/destructive/apply-live
+++ b/tests/kolainst/destructive/apply-live
@@ -25,6 +25,13 @@ set -x
 
 cd $(mktemp -d)
 
+# apply-live is not yet compatible with state overlays
+# https://github.com/coreos/rpm-ostree/pull/4810#issuecomment-1939351259
+if jq -e '.["opt-usrlocal-overlays"]' /usr/share/rpm-ostree/treefile.json; then
+    echo "skip apply-live does not work currently with state overlays"
+    exit 0
+fi
+
 case "${AUTOPKGTEST_REBOOT_MARK:-}" in
 "")
 
diff --git a/tests/kolainst/destructive/cliwrap b/tests/kolainst/destructive/cliwrap
index fc64a29099..7f2b578d29 100755
--- a/tests/kolainst/destructive/cliwrap
+++ b/tests/kolainst/destructive/cliwrap
@@ -27,9 +27,13 @@ libtest_prepare_offline
 libtest_enable_repover 0
 cd $(mktemp -d)
 
+case "${AUTOPKGTEST_REBOOT_MARK:-}" in
+"")
 rpm-ostree deploy --ex-cliwrap=true
-rpm-ostree apply-live  # yep it works!
+/tmp/autopkgtest-reboot 1
+;;
 
+1)
 wrapdir="/usr/libexec/rpm-ostree/wrapped"
 if ! test -d "${wrapdir}"; then
     fatal "Missing ${wrapdir}"
@@ -67,3 +71,7 @@ rpm -qa >/dev/null
 rpm --verify bash >out.txt || true
 assert_not_file_has_content "ostree-based"
 echo "ok cliwrap undo"
+;;
+
+*) echo "unexpected mark: ${AUTOPKGTEST_REBOOT_MARK}"; exit 1;;
+esac