Years after fanny packs became cool again, they can get a chilly reception when it’s time to board a plane.

That’s because some travelers test the limits of airline policy and luggage fees by wearing a small bag in addition to toting the permitted number of carry-ons. On most airlines, travelers are not charged for a bag that fits overhead and one under the seat, while many budget carriers charge for anything larger than a smallish under-seat personal item.