Excessive power consumption emerged as a major obstacle to achieving exascale performance in next-generation supercomputers, creating a need to explore new ways to reduce those requirements. In this study, we present a comprehensive empirical investigation of a power advantage anticipated in the mergesort method based on identifying a feature expected to be physically power efficient. We use a highperformance quicksort as a realistic baseline to compare. Results show a generic mergosort to have a distinct advantage over an optimized quicksort lending support to our expectation. They also help develop some insights toward power efficiency gains likely meaningful in a future exascale context where trading some of the abundant performance for much needed power savings in a ubiquitous computation may prove interesting.