A distributed Web system, consisting of multiple servers for data retrieval and a Domain Name Server (DNS) for address resolution, can provide the scalability necessary to keep up with growing client demand at popular sites. However, balancing the requests among these atypical distributed servers opens interesting new challenges. Unlike traditional distributed systems in which a centralized scheduler has full control of the system, the DNS controls only a small fraction of the requests reaching the Web site. This makes it very difficult to avoid overloading situations among the multiple Web servers. We adapt traditional scheduling algorithms to the DNS, propose new policies, and examine their impact. Extensive simulation results show the advantage of using strategies that schedule requests on the basis of the origin of the clients and very limited state information, such as whether a server is overloaded or not. Conversely, algorithms that use detailed state information often exhibit the worst performance.