diff --git a/R/run-tests.sh b/R/run-tests.sh
index 29764f48bd156a97f082b3b13d2b1420026213f1..f38c86e3e6b1dc89a3d6da03d7c4d3b5bff8603b 100755
--- a/R/run-tests.sh
+++ b/R/run-tests.sh
@@ -38,6 +38,7 @@ FAILED=$((PIPESTATUS[0]||$FAILED))
 NUM_CRAN_WARNING="$(grep -c WARNING$ $CRAN_CHECK_LOG_FILE)"
 NUM_CRAN_ERROR="$(grep -c ERROR$ $CRAN_CHECK_LOG_FILE)"
 NUM_CRAN_NOTES="$(grep -c NOTE$ $CRAN_CHECK_LOG_FILE)"
+HAS_PACKAGE_VERSION_WARN="$(grep -c "Insufficient package version" $CRAN_CHECK_LOG_FILE)"
 
 if [[ $FAILED != 0 || $NUM_TEST_WARNING != 0 ]]; then
     cat $LOGFILE
@@ -46,9 +47,10 @@ if [[ $FAILED != 0 || $NUM_TEST_WARNING != 0 ]]; then
     echo -en "\033[0m"  # No color
     exit -1
 else
-    # We have 2 existing NOTEs for new maintainer, attach()
-    # We have one more NOTE in Jenkins due to "No repository set"
-    if [[ $NUM_CRAN_WARNING != 0 || $NUM_CRAN_ERROR != 0 || $NUM_CRAN_NOTES -gt 3 ]]; then
+    # We have 2 NOTEs for RoxygenNote, attach(); and one in Jenkins only "No repository set"
+    # For non-latest version branches, one WARNING for package version
+    if [[ ($NUM_CRAN_WARNING != 0 || $NUM_CRAN_ERROR != 0 || $NUM_CRAN_NOTES -gt 3) &&
+          ($HAS_PACKAGE_VERSION_WARN != 1 || $NUM_CRAN_WARNING != 1 || $NUM_CRAN_ERROR != 0 || $NUM_CRAN_NOTES -gt 2) ]]; then
       cat $CRAN_CHECK_LOG_FILE
       echo -en "\033[31m"  # Red
       echo "Had CRAN check errors; see logs."