This has been theoretically possible for a long time, and in 2005, just before coming to China, I spent weeks trying to satisfy the Cuban and U.S. paperwork and preclearance requirements for flying a Cirrus SR-20 to Havana on a Christmas trip. I finally ran out of patience and time. But now...
Grady's podcast interview with the CEO of the company organizing the trips is here; that company's site is here. And for lessons there are little airports all over the place in the US. I'd be signing up for the trip if I were on that side of the world. Just trying to be constructive here.
This article available online at:
http://www.theatlantic.com/technology/archive/2009/05/still-on-the-fence-about-those-flying-lessons/16985/
