Can dogs fly...?

We are looking into taking our American dogs (my wife is American and so three of our family dogs reside in the US) to our home in Ireland. The last time we considered doing this I did quite a bit of research and became so worried about their welfare that I gave it up. Now I have been introduced to Dana at Pet Movers (dana@petmovers.com) and she has been so reassuring about the whole thing that we are on for it again. She says that the secret is a) use only airports and airlines that treat the dogs as live cargo and not as luggage and b) get prior approval for everything so that there is minimal delay. She warned me against giving the dogs sedatives (which one vet had been suggesting) as it can endanger their health at altitude and told me that not once - ever - has she come across a dog that didn't recover quickly from the experience. It looks as if our dogs will fly after all!