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Description: One major class of approaches to explaining the distribution of linguistic forms is rooted in communicative efficiency. For theories in which the communicative efficiency of an utterance is itself dependent on the distribution of linguistic forms in the language, however, it is less clear how to make distributional predictions that escape circularity. We propose an approach to making distributional predictions for these cases by iterating between speaker and listener in the Rational Speech Act theory. Characteristics of the fixed points of this iterative process constitute the distributional predictions of the theory. Through computer simulation we apply this approach to the well-studied case of predictability-sensitive optional function word omission for the theory of Uniform Information Density, and show that the approach strongly predicts the negative correlation between phrase onset probability and rate of function word use that has previously been argued for and that has been empirically observed in previous studies.