Quality of service (QoS) is one of the key features for new Internet-based multimedia and other applications. Meanwhile, energy remains as a big concern for systems that perform such applications. We address the issue of combining system design concerns and QoS requirements to design systems that can deliver QoS guarantees. In this paper, we discuss how to satisfy QoS requirements and minimize the system's energy consumption. Speci cally, we consider the following problem: Given a set of applications each specifying its required amount of computation and service time, how we allocate CPU time and determine the voltage pro le on a variable voltage system, such that all the applications' requirements are satis ed and the system's total energy consumption is minimized. We optimally solve several basic cases and propose a dynamic programming procedure for the general case. Simulation shows that the new approach saves 38.75% energy over the system shut-down technique.