diff --git a/tools/check_for_upgrade.sh b/tools/check_for_upgrade.sh
index a9d74acf6..73bfd39f5 100644
--- a/tools/check_for_upgrade.sh
+++ b/tools/check_for_upgrade.sh
@@ -57,7 +57,7 @@ function is_update_available() {
     (builtin cd -q "$ZSH"; LANG= git fetch --quiet $remote $branch) || return 1
     zmodload zsh/datetime
     cutoff_epoch=$(( EPOCHSECONDS - cooldown_days * 86400 ))
-    cooldown_ref=$(builtin cd -q "$ZSH"; git log --format="%H %ct" FETCH_HEAD \
+    cooldown_ref=$(builtin cd -q "$ZSH"; git log --first-parent --format="%H %ct" FETCH_HEAD \
       | awk -v c="$cutoff_epoch" '$2 <= c { print $1; exit }')
     [[ -n "$cooldown_ref" ]] || return 1
     [[ "$cooldown_ref" != "$local_head" ]] || return 1
diff --git a/tools/upgrade.sh b/tools/upgrade.sh
index 705de3f65..93df90dd7 100755
--- a/tools/upgrade.sh
+++ b/tools/upgrade.sh
@@ -248,7 +248,7 @@ update_with_cooldown() {
   cutoff_epoch=$(( EPOCHSECONDS - cooldown_days * 86400 ))
   LANG= git fetch --quiet $remote $branch || return $?
 
-  cooldown_ref=$(git log --format="%H %ct" FETCH_HEAD \
+  cooldown_ref=$(git log --first-parent --format="%H %ct" FETCH_HEAD \
     | awk -v c="$cutoff_epoch" '$2 <= c { print $1; exit }')
 
   [[ -n "$cooldown_ref" ]] || return 0