We interpret the discriminatory power, r, in the Power Contest Success Function (Tullock, 1980) as the contest designer's accuracy level. We look at the cases where two contestants are heterogeneous in ability and construct an equilibrium set for r > 0. We find that if the contestants are sufficiently different in ability, there always exists an optimal accuracy level for the contest designer. Additionally, as the difference in their abilities increases, the optimal accuracy level decreases.