There are certainly some great films in that list. But most of those films aren't necessarily "independent," so Depp deserves even more credit for trying "off-beat" themes while working within the overall structure.

The Brave, which played In-Competition at Cannes in 1997 is still not available in this country in any format. It is Depp's only directorial effort so far. From what I've read, this was a very personal film so he was hurt by the non-reaction from the community here. Depp plays a downtrodden American-Indian who gets offered a part in a snuff film (perhaps that's the way his career went early on), and he has to make various decisions considering money and ethics. It's no masterpiece, but it is well-acted and shot. Brando has a small role.