When scheduling to minimize the sojourn time tail, the goals of optimality and robustness are seemingly at odds. Over the last decade, results have emerged which show that scheduling disciplines that are near-optimal under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and vice-versa. Very recently, it has been shown that this conflict between optimality and robustness is fundamental, i.e., no policy that does not learn information about the workload can be optimal across both light-tailed and heavytailed workloads. In this paper we show that one can exploit very limited workload information (the system load) in order to design a scheduler that provides robust performance across heavy-tailed and light-tailed workloads. ©2010 IEEE.