This paper addresses the concurrent task management of complex multi-media systems, like the MPEG4 IM1 player, with emphasis on how to derive energy-cost vs time-budget curves through task scheduling on a multi-processor platform. Starting from the original "standard" specification, we extract the concurrency originally hidden by implementation decisions in a "grey-box" model. Then we have applied two high-level transformations on this model to improve the task-level concurrency. Finally, by scheduling the transformed task-graph, we have derived energy-cost vs time-budget curves. These curves will be used to get globally optimized design decisions when combining subsystems into one complete system or to be used by a dynamic scheduler. The results on the MPEG4 IM1 player confirm the validity of our assumptions and the usefulness of our approach.