I washed my white AF shirt by hand, and it came out great. It is a cotton spandex blend with cotton organza puff sleeves, and I didn't even need to iron it, just laid it flat to dry. I suspect my black top will be same, although, it will probably still need some light pressing because it's a woven cotton.
Most of the my other items I wash in a lingerie bag, and air dry--they come out great. Silk stuff I have to dry clean. I am going to see if I can find a better cleaner though, and possibly request that they not press anything (I feel better doing that myself anyway, and don't mind ironing). To freshen dry clean only items, I have been doing as Shiny suggested and using Dry-el. That has been working wonderfully.