Even swaps is a method for solving deterministic multi-attribute decision problems where the decision maker iteratively simplifies the problem until the optimal alternative is revealed (Hammond et al. 1998, 1999). We present a new practical decision support system that takes a Bayesian approach to guiding the even swaps process, where the system makes queries based on its beliefs about the decision maker's preferences and updates them as the interactive process unfolds. Through experiments, we show that it is possible to learn enough about the decision maker's preferences to measurably reduce the cognitive burden, i.e. the number and complexity of queries posed by the system.