I don't know what airline you took, but I flew with my bike from Italy to Chicago, and I just removed the tires and stuck it in the bike luggage. I flew Swiss Air and questioned them extensively, and they not only DIDN'T charge me a dime, they took pride in exclaiming that they are knowledgeable with shipping bikes in their planes. They hand carried my bike to the plane and when I got home, I was so nervous, but there wasn't a scratch on the bike, nor were their dents, knicks, etc. The bike rode like a dream.
I've always had problems with American, United, Alitalia, and Air France with my Specialized bike. There was always a mechanical problem that really messed my bike up once I got to my destination. In one case, it was almost unrideable.... actually, it was unrideable. I couldn't ride more than 10 miles per hour. In every case but one, I used the hard shell Performance luggage. The time I took Swiss Air with my road bike, I just had the soft shell luggage.
I never have problems with my Bike Friday and the luggage it comes in. In one case, I was horrified to see the bike shoot out of the luggage bin when I was waiting for my other luggage at the luggage pick up. I was sure they were going to put it with oversized luggage, but instead, they loaded it up with the other luggage and threw it down the luggage bin. But I never had a problem with the bike, even when it was deposited back to my possesion in that manner.
Koffee