Low-power and energy-efficient system implementations have become very important design issues to extend operation duration or cut power bills. To balance the energy consumption resulting from the dynamic power consumption and the static power consumption, the concept of critical speed has been adopted widely in the literature. Most scheduling algorithms for such systems assume that the critical speed is the lowest speed for scheduling and then perform job/task procrastination to turn the processor(s) to the dormant mode when there is no job for execution. This paper shows that the critical speed might be too optimistic and turning the processor(s) to the dormant mode might be energy-inefficient. By allowing tasks to run at lower speeds than the critical speed, in this paper, a new approximation algorithm is developed for homogeneous