Proposals for improving the performance of Peer-to-Peer file sharing systems like Gnutella often simply involve changes to the distributed search protocol. Since the effectiveness of any routing protocol is dependent on the P2P overlay network's interconnection topology, simultaneously controlling the network topology should enable performance enhancements as well. We consider how locally adaptive behaviors can lead to globally robust, scalable, and efficient P2P networks. We adapt topologies using operations of edge thinning, the removal of redundant links based on message passing utilities, and diameter folding, the selective addition of short-cut links between nodes at or near the diameter of the graph. Using network simulations, we establish how these locally selfish behaviors might help explain the ubiquitous natural occurrence of scale-free networks, and demonstrate how P2P networks that adapt their topologies toward more regular degree distributions improve in both performance and robustness.