A dynamic priority discipline, 'Head-of-the-Line with Priority Jumps', is proposed as an efficient link schedule for a packet switch serving multiple classes of delay-sensitive traffic. Implementation of this discipline is considered to be relatively simple, and the processing overhead relatively small. It is shown that, by properly adjusting the control parameters, the discipline can: (I) satisfy any relative average delay requirements for the different classes, thus bringing fairness of service, and resulting in resource saving, and (II) make the tail probability of the delay distributions for the different classes beyond their target maximum delays approximately the same, thus approximately minimizing the overall maximum tail probability in the system.