Some cases may fit in some overheads, but when I went to France with a bari, it was quite clear that my friend's tenor barely fit. There was no way the bari would have fit. If I had to do it again, I'd pack my bari for shipping (case inside a box with insulation) and plan on storing or discarding the packing at the destination. My bari was sent in the cargo hold in the much-maligned Walt Johnson case. I had no issues with its condition at arrival, though it was a day late returning after being mis-routed in US Customs.