Optimally allocating cellphone spectrum, advertisements on the Internet, and landing slots at airports is computationally intractable. When the participants may strategize, not only must the optimizer deal with complex feasibility constraints but also with complex incentive constraints. We give a very simple method for constructing a Bayesian incentive compatible mechanism from any, potentially non-optimal, algorithm that maps agents' reports to an allocation. The expected welfare of the mechanism is, approximately, at least that of the algorithm on the agents' true preferences.