When accounting for the usage of some linguistic form, one can refer to its discourse profile, all concomitant features frequently co-occurring with that form in discourse, or abstract a more general claim about its discourse function, referring only to the necessary and sufficient conditions for the proper occurrence of the form. This article discusses discourse profile and discourse function approaches to referring expressions in linguistic and psycholinguistic research. Focusing on English prenominal possessive noun phrases (NPs, e.g., my career), I argue that although their (prototypical) discourse profile is amenable to clearly defined automatic processing or production cues, and to explaining potential grammaticizations, only their discourse functions can account for all the forms actually attested in discourse. I conclude that both types of accounts are linguistically relevant, and I propose that psycholinguists devise experiments to test the three hypotheses outlined (discourse profiles, discourse functions, and a combination of discourse profiles and discourse functions).