What makes a question useful? What makes an answer appropriate? In this paper, we formulate a family of increasingly sophisticated models of question-answer behavior within the Rational Speech Act framework. We compare these models based on three different pieces of evidence: first, we demonstrate how our answerer models capture a classic effect in psycholinguistics showing that an answerer's level of informativeness varies with the inferred questioner goal, while keeping the question constant. Second, we jointly test the questioner and answerer components of our model based on empirical evidence from a question-answer reasoning game. Third, we examine a special case of this game to further distinguish among the questioner models. We find that sophisticated pragmatic reasoning is needed to account for some of the data. People can use questions to provide cues to the answerer about their interest, and can select answers that are informative about inferred interests.