Dynamic Power Management (DPM) techniques are crucial in minimizing the overall energy consumption in real-time embedded systems. The timing constraints of real-time applications and non-trivial time/energy transition overheads introduce significant challenges, as the device sleep intervals should be longer than a minimum threshold (called the break-even time) to ensure energy-efficiency. In this paper, we present a novel approach to the real-time DPM problem, by explicitly enforcing long device sleep intervals for different devices, called device forbidden regions. We focus on the application of our technique to task systems with Rate-Monotonic priorities, and develop our algorithm DFR-RMS. Our solution includes a static component where the duration and frequency of forbidden regions are determined through the extended time-demand analysis to preserve the temporal correctness of all the tasks, while enhancing the energy savings. Then, we present a sophisticated on-line component wh...