Maximize Presupposition! is an economy condition that adjudicates between contextually equivalent competing structures. Building on data discovered by O. Percus, I will argue that the constraint is checked in the local contexts of embedded constituents. I will argue that this architecture leads to a general solution to the problem of antipresupposition projection, and also allows I. Heim's ' Novelty/Familiarity Condition' to be eliminated as a constraint on operations of context change.