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Many embedded systems such as PDAs require processing of the given applications with rigid power budget. However, they are able to tolerate occasional failures due to the imperfect human visual/auditory systems. The problem we address in this paper is how to utilize such tolerance to reduce multimedia system's energy consumption for providing guaranteed quality of service at the user level in terms of completion ratio. We explore a range of offline and on-line strategies that take this tolerance into account in conjunction with the modest non-determinism in application's execution time. First, we give a simple best-effort approach that achieves the maximum completion ratio; then we propose an enhanced on-line best-effort energy minimization (BEEM) approach and a hybrid offline/on-line minimum effort (O2 ME) approach. We prove that BEEM maintains the maximum completion ratio while consuming the probably least amount of energy and O2 ME guarantees the required completion ratio statistically. We apply both approaches to a variety of benchmark task graphs, most from popular DSP applications. Simulation results show that significant energy savings (38% for BEEM and 54% for O2 ME, both over the simple best-effort approach) can be achieved while meeting the required completion ratio requirements.