Power efficient design of real-time systems based on programmable processors becomes more important as system functionality is increasingly realized through software. This paper presents a powerefficient version of a widely used fixed priority scheduling method. The method yields a power reduction by exploiting slack times, both those inherent in the system schedule and those arising from variations of execution times. The proposed run-time mechanism is simple enough to be implemented in most kernels. Experimental results show that the proposed scheduling method obtains a significant power reduction across several kinds of applications.