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Distributed Hash Table (DHT) based peer-to-peer overlays are decentralized, scalable, and fault tolerant. However, due to their decentralized nature, it is very hard to know the state and prevailing operating conditions of a running overlay. If the system could figure out the operating conditions, it would be easier to monitor the system and re-configure it in response to changing conditions. Many DHT-based system such as the Peer-to-Peer Session Initiation Protocol (P2PSIP) would benefit from the ability to accurately estimate the prevailing operating conditions of the overlay. In this paper, we evaluate mechanisms that can be used to do this. We focus on network size, join rate, and leave rate. We start from existing mechanisms and show that their accuracy is not sufficient. Next, we show how the mechanisms can be improved to achieve a higher level of accuracy. The improvements we study include various mechanisms improving the accuracy of leave rate estimation, use of a secondary network size estimate, sharing of estimates between peers, and statistical mechanisms to process shared estimates.