Current world-wide web servers as well as proxy servers rely for their scheduling on services provided by the underlying operating system. In practice, this means that some form of first-come-first-served (FCFS) scheduling is utilised. Although FCFS is a reasonable scheduling strategy for job sequences that do not show much variance, in the world-wide web (WWW), however, it has been shown that the typical object sizes requested do exhibit heavy tails. This means that the probability to observe very long jobs (very large objects) is much higher than typically predicted using an exponential model. Under these circumstances, job scheduling on the basis of shortest-job first (SJF) has been shown to perform much better, in fact, to minimise the total average waiting time, simply by avoiding situations in which short jobs have to wait for very long one. However, SJF has as disadvantage that long jobs might suffer from starvation. In order to avoid the problems of both FCFS and SJF we present in this paper a new scheduling algorithm called class-based interleaving weighted fair queueing (CI-WFQ). This algorithm uses the specific characteristics of the job stream being served, that is, the distribution of the sizes of the objects being requested, to set its parameters such that good mean reponse times are obtained and starvation does not occur. In the paper., the new scheduling approach is introduced and compared, using trace-driven simulations, with existing scheduling approaches.