The wave of electricity market restructuring both within the United States and worldwide has brought the issue of horizontal market power to the forefront. Traditionally, estimation and prediction of market power has heavily relied on concentration measures. In this paper, we discuss the weaknesses of concentration measures as a viable measure of market power in the electricity industry, while proposing an alternative based on market simulations and the use of plant level data. We discuss results from previous studies the authors have performed, and present new results that allow for the detection of threshold demand levels where market power is likely to be a problem. In addition, we analyze the impact the recently proposed divestitures in the California electricity market have on estimated market power. We close with a discussion of the policy implications of the results.