Most recent research in power-aware supercomputing has focused on making individual nodes more efficient and measuring the results in terms of flops per watt. While this work is vital in order to reach exascale computing at 20 megawatts, there has been a dearth of work that explores efficiency at the whole system level. Traditional approaches in supercomputer design use worst-case power provisioning: the total power allocated to the system is determined by the maximum power draw possible per node. In a world where power is plentiful and nodes are scarce, this solution is optimal. However, as power becomes the limiting factor in supercomputer design, worst-case provisioning becomes a drag on performance. In this paper we demonstrate how a policy of overprovisioning hardware with respect to power combined with intelligent, hardware-enforced power bounds consistently leads to greater performance across a range of standard benchmarks. In particular, leveraging overprovisioning requires that applications use effective configurations; the best configuration depends on application scalability and memory contention. We show that using overprovisioning leads to an average speedup of more than 50% over worst-case provisioning.