The Internet's current numbering system is nearing exhaustion: Existing protocols allow only a finite set of computer numbers ("IP addresses"), and central authorities will soon deplete their supply. I evaluate a series of possible responses to this shortage: Sharing addresses impedes new Internet applications and does not seem to be scalable. A new numbering system ("IPv6") offers greater capacity, but network incentives impede transition. Paid transfers of IP addresses would better allocate resources to those who need them most, but unrestricted transfers might threaten the Internet's routing system. I suggest policies to facilitate an IP address "market" while avoiding major negative externalities - mitigating the worst effects of v4 scarcity, while obtaining price discovery and allocative efficiency benefits of market transactions.