In this paper, we address the problem of localizing faults by analyzing execution traces of successful and unsuccessful invocations of the application when run against a suite of tests. We present a new algorithm, based on a linear programming model, which is designed to be particularly effective for the case where multiple faults are present in the application under investigation. Through an extensive empirical study, we show that in the case of both single and multiple faults, our approach outperforms a host of prominent fault localization methods from the literature.