I was looking into the pets policy of Middle Eastern carriers years ago, and was amazed to find that virtually all of them permitted uncaged falcons in the cabin. At the time, most required all other animals to fly in the cargo hold.

Royal Jordanian's pet policy is here: http://www.rj.com/TravelEssentials/P...S/default.aspx - the section about falcons is at the end. Most regional airlines have similar rules. I've never actually seen it, though.

Setting aside the inconvenience to other passengers, well-trained falcons are worth a fair amount of money. If I'd made that investment, I wouldn't want to take the chance of the bird panicking and hurting itself, which it could easily do while leg-tethered to a seat. The bird would be much safer (and probably happier) in a cage.