Proxy bidding has proven useful in a variety of real auction formats – most notably eBay – and has been proposed for the nascent field of combinatorial auctions. Previous work on proxy bidding in combinatorial auctions requires the auctioneer to run the auction with myopic bidders to determine the outcome. In this paper, we present a radically different approach that computes the bidders’ allocation of their attention across the bundles only at “inflection points”. Inflections are caused by the introduction of a new bundle into an agent’s demand set, a change in the set of currently competitive allocations, or the withdrawal of an agent from the set of active bidders. This approach has several advantages over alternatives, including that it computes exact solutions and is invariant to the magnitude of the bids.