Utilizing customers' service-time information, we study an easy-to-implement scheduling policy with two priority classes. By carefully designing the classes, the two-class priority rule achieves near-optimal performance. In particular, for a single-server queue, as the traffic intensity approaches 1, the policy achieves a scaling for the queue length processes that is similar to the shortest remaining processing time first policy. Our analysis quantifies how the tail of the service time distribution affects the benefits one can gain from service-time-based scheduling policies. When the service times are misspecified, we further quantify how imperfect observation of the service time affects the performance of the two-class priority rule through both theoretical and numerical analysis. Our results demonstrate the robustness of the two-class priority rule. Specifically, even with imperfect service-time information, the two-class priority rules can still achieve substantial performance improvement over the first come first served.