There is a standard way of interpreting physicalism. This is as a completeness thesis of some kind. Completeness physicalists believe there is or in principle could be some future physics that provides a complete explanatory or ontological basis for our universe. And this provides a sense in which physics is special among the sciences, the sense in which it is fundamental. This paper contrasts this standard completeness physicalism with what is a more plausible maximality physicalism. Maximality physicalists believe physics is (...) special only in its providing an epistemic framework that is ontologically or explanatorily superior in some respect. This paper shows how completeness physicalists cannot, while maximality physicalists can, provide an adequate explanation of the empirical support for and the pragmatic usefulness of physicalism. It also shows how maximality physicalism is better supported in light of several developments from late twentieth century philosophy of science. (shrink)