We use laboratory experiments to test models of rational inattention, in which people acquire information to maximize utility net of information costs. We show that subjects adjust their attention in response to changes in incentives, in line with the rational inattention model. However, our results are qualitatively inconsistent with information costs that are linear in Shannon entropy, as is often assumed in applied work. Our data are best fit by a generalization of the Shannon model, which allows for a more flexible response to incentives and for some states of the world to be harder to distinguish than others.