Abstract We study the problem of designing efficient auctions where bidders have interdependent values; i.e., values that depend on the signals of other agents. We consider a contingent bid model in which agents can explicitly condition the value of their bids on the bids submitted by others. In particular, we adopt a linear contingent bidding model for single minded combinatorial auctions (CAs), in which submitted bids are linear combinations of bids received from others. We extend the existing state of the art, by identifying constraints on the interesting bundles and contingency weights reported by the agents which allow the efficient second priced, fixed point bids auction to be implemented in single minded CAs. Moreover, for domains in which the required single crossing condition fails (which characterizes when efficient, IC auctions are possible), we design a two-stage mechanism in which a subset of agents (“experts”) are allocated first, using their reports to allocate the remaining items to the other agents.