According to a large, influential psychological literature, humans are predictably irrational. Proponents of the heuristics-and-biases programme argue that our mental software leads us to diverge from elementary principles of probability and decision theory. Similarly, reasoning scientists have catalogued surprising human errors in drawing basic logical inferences. However, insights from Bayesian cognitive science appear to recommend a more optimistic evaluation of human rationality, highlighting our exquisite sensitivity to the statistical structure of the environment and the laws of probability theory. Does Bayesian cognitive science vindicate us of the charge of irrationality that the heuristics-and-biases approach levels? I argue that Bayesian cognitive science paints a picture of the mind-brain as more intelligent, more subtle, more sophisticated and more sensitive to context than that painted by heuristics-and-biases psychology, however it does not ultimately vindicate us of the charge of systematic irrationality that the heuristics-and-biases paradigm levels.