One of the main characteristics of the peer-to-peer systems is the highly dynamic nature of the users present in the system. In such a rapidly changing enviroment, end-user guarantees become hard to handle. In this paper, we propose a search-theoretic view for performing lookups. We define a new search mechanism with cost-analysis for refining the lookups by predicting the arrival and leave possibilities of the users. Our system computes a threshold for the number of times that a user has to perform. We compare our results with the naive approach of accepting the first set of results as the basis.