 Lewis (1979) argues that properties/centered-worlds propositions can do all of the attitude-characterizing work of traditional possible-worlds propositions, and more besides. For each possible-worlds proposition P, there’s a corresponding property (centered-worlds proposition)—the property of inhabiting a P-world, a.k.a. the set of triples \(\langle w,t,i\rangle\) such that \(w\) is a P-world. But there are also more properties and centered-worlds propositions—ones that sometimes distinguish between worldmates, such that one individual in a world has the property and another doesn’t, or such that an individual in a world has the property at some times but not others. Let’s call the first kind of property or centered proposition boring and the second kind interesting. Where a possible-worlds proposition would do as an object of belief, the corresponding boring property or centered proposition will do as well (see Nolan 2006 for dissent, and Turner 2010 and Feit 2010 for defense). So every doxastic state that we could represent using belief relations to possible-worlds propositions—every one that appeared in the Simple Picture—we can also represent using belief relations to boring properties or boring centered propositions. But having properties or centered propositions as objects of belief gives us additional resources we can use to represent doxastic states that resisted characterization using the Simple Picture.