This work presents a dynamic voltage and frequency scaling (DVFS) technique that minimizes the total system energy consumption for performing a task while satisfying a given execution time constraint. We first show that in order to guarantee minimum energy for task execution by using DVFS it is essential to divide the system power into active and standby power components. Next, we present a new DVFS technique, which considers not only the active power, but also the standby component of the system power. This is in sharp contrast with previous DVFS techniques, which only consider the active power component. We have implemented the proposed DVFS technique on the BitsyX platform - an Intel PXA255-based platform manufactured by ADS Inc., and report detailed power measurements on this platform. These measurements show that, compared to conventional DVFS techniques, an additional system energy saving of up to 18% can be achieved while satisfying the user-specified timing constraints.