Stassen (2009) points out a set of possession constructions in which the possessee appears as the predicate in a copular construction. In these constructions, the possessee appears to be marked by a derivational morpheme, often an adjectivalizer or nominalizer. An example is the English –ed in contexts like John is blue-eyed. Stassen dubs this phenomenon Predicativization. In this chapter, I show that Predicativization cannot be related to more familiar types of HAVE or BE construction by movement, further undermining the Freeze/Kayne tradition. This is shown via a detailed analysis of the –yoq suffix in Cochabamba Quechua, in which Delayed Gratification plays a key role. Drawing on and amending ideas from Nevins and Myler (2014, submitted), the chapter then lays out a detailed typology of Predicativization structures cross-linguistically. The main parameters of variation in this typology are (i) the category of the Predicativizing morpheme itself, (ii) the size of the nominal substructure it selects, (iii) whether it requires modifier, and (iv) whether or not the modifier can be phrasal.