In this paper, which discusses data from Gargano Apulian Italo-Romance, I propose that prepositional and non-prepositional genitives are fundamentally two different types of phrases, and that the interpretation of a non-prepositional noun as the possessor is not due to a silent preposition or head-modifier inversion, but rather to an agreement mechanism taking place between the modifier and its head. We propose that, just as a genitive can agree with its head for gender and number features so it can for definiteness, and that agreement for definiteness yields a genitival interpretation of the non-prepositional noun. I.e., definiteness can externalize the syntactic relation between head and modifier. We also propose that in this Apulian variety, non-prepositional genitives are syntactic phases (Chomsky 2001), and that the same holds for non-prepositional ‘qualitative’ predicative phrases in the same language. This would explain the impossibility of accessing the phrase through syntactic operations such as extraction.