A review of recent literature reflects the development of several deterministic nonparametric market power tests. We use Monte Carlo experiments to evaluate the veracity of four monopolistic and four monopsonistic market power tests that use the deterministic nonparametric approach. The experiments are implemented using data from ten known market structures. When results are compared to Raper, Love, and Shumway's (1999) findings concerning parametric market power tests in the Bresnahan-Lau tradition, we find that the parametric tests perform well while only two of the nonparametric tests appear able to identify market power.