Most current peer-to-peer lookup schemes keep a small amount of routing state per node, typically logarithmic in the number of overlay nodes. This design assumes that routing information at each member node must be kept small, so that the bookkeeping required to respond to system membership changes is also small, given that aggressive membership dynamics are expected. As a consequence, lookups have high latency as each lookup requires contacting several nodes in sequence. In this paper, we question these assumptions by presenting two peer-to-peer routing algorithms with small lookup paths. First, we present a one-hop routing scheme. We show how to disseminate information about membership changes quickly enough so that nodes maintain accurate routing tables with complete membership information. We also deduce analytic bandwidth requirements for our scheme that demonstrate its feasibility. We also propose a two-hop routing scheme for large scale systems of more than a few million nodes,...