We consider market rules for transferring IP addresses, numeric identifiers required by all computers connected to the Internet. Transfers usefully move resources from lowest to highest-valuation networks, but transfers tend to cause socially costly growth in the Internet's routing table. We propose a market rule that avoids excessive trading and comes close to achieving social efficiency. We argue that this rule is feasible despite the limited powers of central authorities. We also offer a framework for reasoning about future prices of IP addresses, then explore the role of rentals in sharing information about the value of IP address and assuring allocative efficiency.