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We study the threat that passive logging attacks pose to anonymous communications. Previous work analyzed these attacks under limiting assumptions. We first describe a possible defense that comes from breaking the assumption of uniformly random path selection. Our analysis shows that the defense improves anonymity in the static model, where nodes stay in the system, but fails in a dynamic model, in which nodes leave and join. Additionally, we use the dynamic model to show that the intersection attack creates a vulnerability in certain peer-to-peer systems for anonymous communications. We present simulation results that show that attack times are significantly lower in practice than the upper bounds given by previous work. To determine whether users' Web traffic has communication patterns required by the attacks, we collected and analyzed the Web requests of users. We found that, for our study frequent and repeated communication to the same Web site is common.