Much of our interpersonal communication conforms to Gricean-style norms governing the truthfulness, informativeness and relevance of the information exchanged. But we also experience untruthful, uninformative, and misleading communication when these norms are violated. How do people draw upon this experience when attempting to conceal the truth? We introduce a computational model which predicts how people should best conceal the truth when required to reveal information to another (and lying is not an option). We argue that when placed in such situations, people will take into account the other’s expectations of whether Gricean norms apply. This notion is incorporated in our model, which we test with an experiment that manipulates people’s assumptions in this regard. Results show that revealing informative but misleading information is an acceptable strategy when the other expects cooperation; otherwise, being uninformative is overwhelmingly preferred. We analyse how our model and alternatives account for these results.