No on-line scheduling algorithm operating in an uniprocessor environment can guarantee to obtain a useful processor utilization greater than 0.25 under conditions of overload. This result holds in the general case, where the deadlines of the input tasks can be arbitrarily "tight." We address here the issue of improving overload performance in environments where there is a limit on the tightness of task deadlines. In particular, we present a new scheduling algorithm, ROBUST, that efficiently takes advantage of these limits to provide improved overload performance and is asymptotically optimal. We also introduce the concept of overload tolerance, wherein a system's overload performance never falls below its design capacity, and describe how ROBUST may be used to construct overload tolerant systems.