I searched and didn't find this information here (or really anywhere else online).

But Southwest Airlines informed me upon inquiry that they allow carry-on of any "luggable" instrument so long as (a) there is available bin space, and (b) the instrument is in a SOFT PADDED CASE that fits in the overhead bin (SW is flying larger 737-400s these days, and the o'head bins are a lot bigger than they were a few years ago).

If (a) fails to be the case, you may gate-check the instrument (i.e. the flight attendant takes it from you just before you board the aircraft, and returns it to you as you step off at the end of the flight, so the "baggage apes" never get their paws on it.

Anyway, this has been great for carrying my gig-bagged Cort Parlor guitar back and forth between Houston and Tulsa these last couple of weeks.