How can questions be informative before they are answered?

We examine a special case of inquiry games inspired by Hintikka's interrogative model of inquiry, and give an account of the informational import of asking questions. We focus on yes-no questions, which always carry information about the questioner's strategy, but never about the state of Nature, and show how strategic information reduces uncertainty through inferences about other players' goals and strategies. This uncertainty cannot always be captured by information structures of classical game theory. We conclude on the connection with Gricean pragmatics and contextual constraints on interpretation.