I argue that Äiwoo (Oceanic) doesn’t have real nominal possessives like my or ’s in English. Instead, I show that all possessive constructions involve the presence of a transitive ‘have’-like verb in undergoer voice, whose theme can be extracted. Informally put, “my dogs” is “the dogs [that I have __]”. I discuss implications of this for whether a universal underlying structure for possessive constructions (Freeze 1992, Kayne 1993) can be maintained.