What is the precise meaning of anatta?

This is focusing in on one specific aspect of what was asked here: https://buddhism.stackexchange.com/questions/1854/what-are-the-three-marks-of-existence I often hear "anatta" explained as being an expression of the non-existence of the self. However, various places add an adjective first. For example, I've heard it said that anatta refers to the non-existence of a "permanent" self, or a "material" self, or a "separate" self (or some combination of those and others). It seems clear to me that it cannot mean the non-existence of a self *per se*, because such a statement -- "There is no self" -- would be auto-refuting. So exactly what is meant by anatta?