Journal article: This paper develops a game-theoretic model of "petty corruption" by government officials. Such corruption is widespread, especially (but not only) in developing and transition economies. The model goes beyond the previously published studies in the way it describes the structure of bureaucratic "tracks," and the information among the participants. Entrepreneurs apply, in sequence, to a "track" of two or more bureaucrats in a prescribed order for approval of their projects. Our first result establishes that in a one-shot situation no project ever gets approved. This result leads us to consider a repeated interaction setting. In that context we characterize in more detail the trigger-strategy equilibria that minimize the social loss due to the system of bribes, and those that maximize the expected total bribe income of the bureaucrats. The results are used to shed some light on two much advocated anti-corruption policies: the single window policy and rotation of bureaucrats.