We consider the issue of hemispherical power asymmetry in the third-year WMAP data, adopting a previously introduced modulation framework. Computing both frequentist probabilities and Bayesian evidences, we find that the model consisting of an isotropic CMB sky modulated by a dipole field gives a substantially better fit to the observations than the purely isotropic model, even when accounting for the larger prior volume. For the ILC map, the Bayesian log-evidence difference is ~1.8 in favor of the modulated model, and the raw improvement in maximum log likelihood is 6.1. The best-fit modulation dipole axis points toward (l, b) = (225°, -27°), and the modulation amplitude is 0.114, in excellent agreement with the results from the first-year analyses. The frequentist probability of obtaining such a high modulation amplitude in an isotropic universe is ~1%. These results are not sensitive to data set or sky cut. Thus, the statistical evidence for a power asymmetry anomaly is both substantial and robust, although not decisive, for the currently available data. Increased sky coverage through better foreground handling and full-sky and high-sensitivity polarization maps may shed further light on this issue.