This paper explores the potential benefits to asynchronous task-based execution to achieve high performance under a power cap. Task-graph schedulers can flexibly reorder tasks and assign compute resources to data-parallel (elastic) tasks to minimize execution time, compared to executing step-by-step (bulk-synchronously). The efficient utilization of the available cores becomes a challenging task when a power cap is

imposed. This work characterizes the trade-offs between power and performance as a Pareto frontier, identifying the set of configurations that achieve the best performance for a given amount of power. We present a set of scheduling heuristics that leverage this information dynamically during execution to ensure that the processing cores are used efficiently when running under a power cap. This work examines the behavior of three HPC applications on a 57 core Intel Xeon Phi device, demonstrating a significant performance increase over the baseline.