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We introduce the Distributed Approximative System Information Service (DASIS) as a useful scheme to aggregate approximative information on the state of a peer-to-peer system. We present how this service can be integrated into existing peer-to-peer systems, such as Kademlia and Chord. As a sample application, we show how DASIS can be employed for establishing an effective deterministic join algorithm. Through simulation, we demonstrate that the insertion of peers using DASIS information results in a well-balanced system. Moreover, our join algorithm gracefully resolves load imbalances in the system due to unfortunate biased leaves of peers.