Recent work has constructed economic mechanisms that are both truthful and differentially private. In these mechanisms, privacy is treated separately from truthfulness; it is not incorporated in players’ utility functions (and doing so has been shown to lead to nontruthfulness in some cases). In this work, we propose a new, general way of modeling privacy in players’ utility functions. Specifically, we only assume that if an outcome <i>o</i> has the property that any report of player <i>i</i> would have led to <i>o</i> with approximately the same probability, then <i>o</i> has a small privacy cost to player <i>i</i>. We give three mechanisms that are truthful with respect to our modeling of privacy: for an election between two candidates, for a discrete version of the facility location problem, and for a general social choice problem with discrete utilities (via a VCG-like mechanism). As the number <i>n</i> of players increases, the social welfare achieved by our mechanisms approaches optimal (as a fraction of <i>n</i>).