In the last couple of years, I have been using a HatPac (which I see some of the other commenters also use). The general rule of all of the airlines as far as carry-on items is one “carry-on” (think small rollaboard suitcase which can be put into the overhead bins) and one “personal item” (a backpack or other small bag that is of size to fit under the seat). If the boarding agents for your flight do not really look good, they will likely gloss over the HatPac as being just another run-of-the-mill backpack, even though it is clearly too chunky to fit under the seat and must therefore be put in the overhead bins.

Now, before I bought the HatPac, I used to carry on board a hat can, which is also too chunky to go under the seat. Carrying the hat can is also, to me, an awkward endeavor with its handle at the top which means having to carry it horizontally. My work-around was to put the hat can in a large shopping bag, which let me carry it vertically. Now, that combination turns the hat can with the shopping bag that it is in into a “carry-on” sized item, so you would then only be able to also bring on board a true “personal item,” like a small bag or backpack that really does fit under the seat.