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In most peer-to-peer systems, edge resources self-organize into overlay networks. At the core of Freenet-style peer-to-peer systems are insert and request algorithms that dynamically change the overlay network and replicate files on demand. We ran simulations to test how effective these algorithms are at improving the performance of subsequent queries. Our results show that for the original Freenet algorithms, performance improved less rapidly with a ratio of 99 requests to 1 insert than with an equal number of requests and inserts. This motivated us to design and test the performance of several new request algorithms. By changing the overlay network after failed requests and by further rewarding the fulfillers of successful requests, our new algorithms improved median pathlength by up to a factor of 9.25.