Recent work on peer-to-peer systems has demonstrated the ability to deliver low latencies and good load balance when demand for data items is relatively uniform. We describe a lightweight, adaptive, and system-neutral replication protocol, LAR, that delivers low latencies and good load balance even when demand is heavily skewed. Simulation of LAR in combination with both the Chord and TerraDir systems shows that LAR quickly adapts to non-uniformity in both the underlying system topology and in the input stream. Further, we demonstrate better performance than functionally similar application-layer protocols, using an order of magnitude less network bandwidth. (UMIACS-TR-2003-83)