Differences in cognitive sophistication and effort are at the root of behavioral heterogeneity in economics. To explain this heterogeneity, behavioral models assume that certain choices indicate higher cognitive effort. A fundamental problem with this approach is that observing a choice does not reveal how the choice is made, and hence choice data is insufficient to establish the link between cognitive effort and behavior. We show that deliberation times provide the missing link, in the form of an individually-measurable correlate of cognitive effort. We present a model of heterogeneous cognitive depth, incorporating stylized facts from the psychophysical literature, which makes predictions on the relation between choices, cognitive effort, incentives, and deliberation times. We confirm the predicted relations experimentally in different kinds of games. However, we also show that imputing cognitive depth from choices alone can lead to erroneous conclusions when the features leading to iterative thinking are not salient.