Mix networks and anonymity networks provide anonymous communication via relaying, which introduces overhead and increases the end-to-end message delivery delay. In practice overhead and delay must often be low, hence it is important to understand how to optimize anonymity for limited overhead and delay. In this work we address this question under passive traffic analysis attacks, whose goal is to learn the traffic matrix. For our study, we use two anonymity networks: MCrowds, an extension of Crowds, which provides unbounded communication delay and Minstrels, which provides bounded communication delay. We derive exact and approximate analytical expressions for the relationship anonymity for these systems. Using MCrowds and Minstrels we show that, contrary to intuition, increased overhead does not always improve anonymity. We investigate the impact of the system's parameters on anonymity, and the sensitivity anonymity to the misestimation of the number of attackers. / <p>QC 20130522</p>