The Rational Speech-Act model (RSA; Frank & Goodman, 2012) offers a model of pragmatic reasoning in which speakers try to optimize their utterance in a trade-off between informativity and cost, and listeners retrieve the communication goal of the speaker through Bayesian reasoning. This model has successfully captured a number of linguistic phenomena at the semantics/pragmatics interface, and offers a new formalization of Grice's theory of implicatures (Grice, 1967), in particular the fact that "some" is often understood to imply "not all". However, the model also makes the counter-intuitive prediction that when the prior for an all-situation is high, "some" could in fact convey "all" rather than "not all". Degen et al. (2015) confirmed our intuition that this prediction was not borne out, and proposed a variant of the RSA which addresses the issue by downplaying the importance of priors in the model (de facto departing from the assumption that listeners are Bayesian). In this talk I will discuss another kind of implicature: exhaustivity inferences: If you ask Sue what she had for lunch and she answers "A sandwich", you will usually infer that she had a sandwich and nothing else (i.e., you assume that her answer is exhaustive). I will present a new study which tested the effects of prior beliefs on both production and comprehension in this kind of situation, addressing shortcomings in previous empirical work. The results confirm that participants' behavior is in clear contradiction with the predictions of RSA, for both production and comprehension. The alternative model proposed by Degen et al. captures the data, but it must assume unrealistic values for some of its parameters. I will discuss other alternatives from the literature, and what a satisfying model would have to look like.