The optimal allocation of resources in complex environments—like allocation of dynamic wireless spectrum, cloud computing services, and Internet advertising—is computationally challenging even given the true preferences of the participants. In the theory and practice of optimization in complex environments, a wide variety of special and general purpose algorithms have been developed; these algorithms produce outcomes that are satisfactory but not generally optimal or incentive compatible. This paper develops a very simple approach for converting any, potentially non-optimal, algorithm for optimization given the true participant preferences, into a Bayesian incentive compatible mechanism that weakly improves social welfare and revenue.