Reliability-aware power management (RAPM) schemes have been recently studied to save energy while preserving system reliability. The existing RAPM schemes, however, provision for worst-case execution scenarios and are rather conservative. In this paper, by exploiting the probabilistic execution time information of real-time tasks, we develop an optimistic RAPM scheme. Instead of scheduling a full recovery for tasks whose executions are scaled down, the new scheme puts aside just enough slack to guarantee the required reliability leave while leaving more slack for energy management to achieve better energy savings. The problem is shown to be NP-hard and a novel heuristic algorithm is proposed and evaluated. The simulation results show that the optimistic RAPM scheme performs very well. It achieves energy savings comparable to that of the ordinary (but reliability-ignorant) power management scheme, while maintaining the system reliability as successfully as the conservative RAPM schemes.