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Recently, size-based policies such as SRPT and FSP have been proposed for scheduling requests in Web servers. SRPT and FSP are superior to policies that ignore request size, such as PS, in both efficiency and fairness, given heavy-tailed service times. However, a central assumption that is usually made in implementing size-based policies in a Web server is that the service time of a request is strongly correlated with the size of the file it serves. By collecting Web server trace data taken from the logs of modified Apache Web servers, this paper reveals that the correlation between service time and file size can be quite low, and shows how the performance of SRPT and FSP can be dramatically affected by the weak correlation via trace-driven simulations. In response, we propose and evaluate domain-based scheduling, a simple technique that better estimates connection times by making use of the source IP address of the request. Domain-based scheduling improves SRPT and FSP performance on Web servers, bringing the performance benefits of these scheduling polices even to those regimes where the correlation between file size and service time is low.