The Federal Deposit Insurance Corporation (FDIC) resolves insolvent banks using an auction process in which bidding is multidimensional and the rule used to evaluate bids along the different dimensions is proprietary. Uncertainty about the scoring rule leads banks to simultaneously submit multiple differentiated bids. This resolution mechanism typically results in considerable losses for the FDIC―$90 billion during the financial crisis. The objective of this paper is to see whether the mechanism could be improved. To do so, we propose a methodology for analyzing auction environments where bids are ranked according to multiple attributes chosen by bidders, but where there is uncertainty about the scoring rule used to evaluate the different components of the bids. Using this framework, which extends structural estimation techniques for combinatorial auctions, and FDIC data summarizing bids, we back out the underlying preferences of banks for failed institutions. With these we perform counterfactuals in which we eliminate uncertainty and/or multiple bidding. Our findings suggest that the FDIC could reduce the cost of resolution by around 17 percent by announcing the scoring rule before bidding begins.