The family tree of cats

Scientists at NCI have delineated the family tree of cats using mitochondrial DNA:

This new history of the family, known as Felidae, is based on DNA analyses of the 37 living species performed by Warren E. Johnson and Stephen J. O'Brien of the National Cancer Institute and colleagues elsewhere.

Now, how about you guys tackle the Psittacidae (parrots)? Of course, there are just over 300 species of parrots, but it would be really interesting to know how they are interrelated. Some work on this has already been done on South American parrots (at least, for macaws, Amazons, Aratingas, caiques, and Pionus), and I think some may have been done on cockatoos as well. It would be really cool to see how other genii fit in. How closely are Pionus and Pionopsitta parrots related? Where do Quaker parrots fit in (are they closer to Aratinga or Pyrruha parakeets)? Are African greys and Eclectus parrots at all related? How about the Tanygnathus parrots? So many questions!