The relevance of the concepts of local syntactic selection and constraints on locally selected dependents in modeling how arguments are syntactically realized has been virtually unchallenged and is assumed to be universal. In this article, we examine more closely these assumptions and ask whether there is anything invariant in the realization of arguments. We argue that the facts of Oneida, and Iroquoian in general, suggest the answer to this question is No . There is no use in Oneida for local selection of phrases realizing semantic arguments (and lexical records of this selection), and words are, as a result, functionally complete. We also argue that there is no use for a level of argument structure or any analogous notion in Oneida. The kinds of processes that justify positing such a level are systematically absent. The facts of Oneida suggest that there is less universality in the syntax/semantics interface (particularly when it comes to the realization of semantic arguments) than is typically assumed and that languages may vary widely in the way semantics is mapped onto syntax. We end with a formal model of the relevant fragment of Oneida within head-driven phrase structure grammar (HPSG).