The budget airlines are getting much tougher on the size of hand baggage......since they started charging for hold baggage more people are taking hand bags only and this has put pressure on cabin locker space.
I took my alto for Stephen's ministrations a coupla weeks ago, but I played safe and packed it, in its Hiscox case, inside my suitcase and padded it with clothes. With my 'full-size carry-on, I had plenty of space.
I was just scared of getting to the gate...where they often now have 'measuring boxes' ....to be told I would have to a)pay extra and b) put the Hiscox, unprotected, in the hold!
(I paid extra, anyway, but not as much).
Another tip I was given at Luton was to get a 'Fragile' sticker on my bag and take it to the 'Outsize Baggage' desk where, they claimed (!) , it would be handled more gently....although it still comes through on the carousel at the other end.
I don't know what I'll do when I need to bring the tenor (Get a bigger suitcase?).
For me it was not a risk worth taking ..... YMMV!
EasyJet also has an option for carrying 'musical instruments' as extras on their booking form....it costs about €23 each way, IIRC, and I don't know what sort of 'special treatment' it gets!