The leading account of intrinsicality over the last thirty years has arguably been David Lewis's account in terms of perfect naturalness. Lewis's account, however, has three serious problems: i) it cannot allow necessarily coextensive properties to differ in whether they are intrinsic; ii) it falsely classifies non-qualitative properties like being Obama as non-intrinsic; and iii) it is incompatible with a number of metaphysical theories that posit irreducibly non-categorical properties. I argue that, as a result of these problems, Lewis's account should (...) be rejected and replaced with an alternative account, which also analyses intrinsicality in terms of perfect naturalness, but which avoids these problems. (shrink)