My guess, without knowing, is that they will check your ticket when you board and if you aren't in the proper class of service, if you take aboard a rolly bag for instance, they are supposed to stop you and make you pay to check it. Of course, that doesn't prevent people from putting the items that do fit under the seat, from them putting them in the overhead. On Allegiant, they charge for carry ons, and it's printed on their tickets, and it's a separate priority boarding group, if you paid for a carry on. I have to say that boarding and deplaning on Allegiant has been the quickest of any airline I've personally flown on recently.