The question of equivalence of constructions with determiner genitives (the FBI's director, the chair's leg) and noun modifiers (the FBI director, the chair leg) is a crucial one for Rosenbach's (2007a, 2010) approach to the gradience between genitive and noun + noun constructions as well as for any study of grammatical variation treating the two constructions as syntactic variants (Szmrecsanyi et al. 2016). However, the assumption that there is such equivalence has recently been challenged by Breban (2018) for English and Schlücker (2013, 2018) for German. The present article defends the view that determiner genitives and identifying noun modifiers are sufficiently similar to alternate in certain choice contexts from a variationist perspective, which, as will be shown, proceeds from a notion of equivalence different from the one adopted by in-depth semantic–pragmatic studies. Proper noun modifiers take a prominent role among identifying noun modifiers in their ability to alternate with determiner genitives, but the argument and analysis in this article is not restricted to them.