SCOTUS hears arguments on pro se representation by the mentally ill

When mentally ill defendants are found competent to stand trial, does that also mean they are competent enough to represent themselves in court?

Tony Mauro, over at Law.com, has this discussion on standard of competence for self-representation. The case concerns a diagnosed as a schizophrenic who was denied his right to represent himself at a 2005 trial for a department store robbery and shooting.