Awerbuch and Scheideler have shown that peer-to-peer overlay networks can survive Byzantine attacks only if malicious nodes are not able to predict what will be the topology of the network for a given sequence of join and leave operations. In this paper we inves- tigate adversarial strategies by following speci c protocols. Our analysis demonstrates rst that an adversary can very quickly subvert overlays based on distributed hash tables by simply never triggering leave operations. We then show that when all nodes (honest and malicious ones) are imposed on a limited lifetime, the system eventually reaches a stationary regime where the ratio of polluted clusters is bounded, independently from the initial amount of corruption in the system.