In the first half of this paper, I argue that essential properties are intrinsic and that this permits a modal analysis of essence that is immune the sort of objections raised by Fine (1994). In the second half, I argue that intrinsic properties collectively have a certain structure and that this accounts for some observations about essences: that things are essentially determinate; that things often have properties within a certain range essentially; and that the essential properties of things are their core properties.