Recently, the so-called class of SMART scheduling policies has been introduced to formalize the common heuristic of "biasing toward small jobs." We study the tail of the sojourn-time (response-time) distribution under both SMART policies and the foreground-background policy (FB) in the GI/GI/1 queue. We prove that these policies behave very well under heavy-tailed service times. Specifically, we show that the sojourn-time tail under all SMART policies and FB is similar to that of the service-time tail, up to a constant, which makes the SMART class superior to first-come-first-served (FCFS). In contrast, for light-tailed service times, we prove that the sojourn-time tail under FB and SMART is larger than that under FCFS. However, we show that the sojourn-time tail for a job of size y under FB and all SMART policies still outperforms FCFS as long as y is not too large. © 2008 INFORMS.