Time-critical jobs in many real-time applications have more than one feasible interval. Such jobs can be executed in any of their feasible intervals. Given a Multiple Feasible Interval (MFI) job set that is schedulable, energy can be saved by carefully selecting the executing interval for each job. In this paper, we explore the energy minimization problem for real-time systems in which jobs have multiple feasible intervals. The static and dynamic energy management schemes are both investigated to minimize the energy consumption while preserving the system’s feasibility. Focusing on the EDF scheduling algorithm, we first study reducing the dynamic power consumption. We show that the static optimal speed assignment problem is NP-Hard and propose a Simulated Annealing (SA) based approach to solve it. Then, we develop an on-line greedy algorithm to exploit the run-time slacks by “fetching” the eligible job from a hot spot to execute earlier, thus, reducing the dynamic energy consumption. In addition, a leakage-aware version is discussed to improve the overall energy efficiency as well. Simulation results show that all the proposed schemes can achieve significant improvements on energy efficiency while the system remains schedulable.