In prior work on multiprocessor fairness, ef?cient techniques with provable properties for reallocating spare processing capacity have been elusive. In this paper, we address this shortcoming by proposing a new notion of multiprocessor fairness, called quick-release fair (QRfair scheduling. Under QRfair scheduling, each task is speci?ed by giving both a minimum and a maximum weight (i.e., processor share. The goal is to schedule each task (as the spare capacity changes at a rate that is (i) at least that implied by its minimum weight and (ii) at most that implied by its maximum weight. We present a quick-release variant of the PD² Pfair scheduling algorithm called PD^Q and prove that the allocations of PD^Q always satisfy (i and (ii . Also, we present results from simulation experiments that show the ef?cacy of PD^Q.