The paper analyzes auctions which are not completely enforceable. In such auctions, the winning bidders may fail to carry out their obligations, and parties involved cannot rely on external enforcement or control mechanisms for backing up a transaction. We propose two mechanisms that make bidders directly or indirectly reveal their trustworthiness. The first mechanism is based on discriminating bidding rules that separate trustworthy from untrustworthy bidders. That is, the auctioneer offers two types of auction rules which are designed so that all trustworthy bidders choose one bidding rule, while untrustworthy bidders choose another. This allows the auctioneer to discover trustworthy bidders and to transact with them. The second mechanism is a generalization of the Vickrey auction to the case of untrustworthy bidders. We prove that, if the winner is considered to have the trustworthiness of the second-highest bidder, truthfully declaring one?s trustworthiness becomes a dominant strategy. We expect the proposed mechanisms to reduce the cost of trust management and to help agent designers avoid many market failures caused by lack of trust.