story identification - Identify an SF novel with references to trillium, telekinesis

I read a book, probably in the late 80s or early 90s, that had several elements. I remember enjoying the book then (it wasn't great art, but it was entertaining), but can't identify it now. The elements I remember was that there was a project called Trillium; there were two or three missiles with horrendous weapons that I believe were telekinetic and I think had American Indian names; the protagonist may have been a rock musician and also had some kind of psychic power. Any idea of the book name and author?