In this cross-linguistic study we present parallels between (a) the stochastic patterns found in corpus studies of English prenominal possessives, and (b) the rule-governed, categorical features of a highly constrained prenominal possessive construction found in some Germanic, Slavic, and Romance languages. The well-known English tendency for prenominal possessor NPs to be low-weight, animate, and discourse-old or highly accessible corresponds to categorical requirements in what we call the Monolexemic Possessor Construction (MLP). This construction is recognizable by its pre-nominal, one-word, animate possessor that is highly accessible in the discourse context. We identify an accessibility hierarchy of nominal categories in which the MLP can be expressed. This hierarchy is consistent with all 17 languages with MLPs we have found. We show that this accessibility hierarchy (pronoun‹ proper noun‹ kinship term‹ common noun) is a function of the intrinsic discourse-pragmatic features of these nominal categories. While the categorical restriction to pronoun and proper noun possessors in Icelandic, German, and Russian may be largely grammaticized, we show that the discourse-pragmatic constraint is recognizably active in Czech and Bosnian/Croatian/Serbian. These results complement studies that attempt to understand how language structure responds to communicative forces and processing constraints.