Standard search and matching models of equilibrium unemployment, once properly calibrated, can generate only a small amount of frictional wage dispersion, i.e., wage differentials among ex-ante similar workers induced purely by search frictions. We derive this result for a specific measure of wage dispersion|the ratio between the average wage and the lowest (reservation) wage paid. We show that in a large class of search and matching models this statistic (the \mean-min ratio") can be obtained in closed form as a function of observable variables (i.e., interest rate, value of leisure, and statistics of labor market turnover). Looking at various independent data sources suggests that, empirically, residual wage dispersion (i.e., inequality among observationally similar workers) exceeds the model's prediction by a factor of 20. We discuss three extensions of the model (risk aversion, volatile wages during employment, and on-the-job search) and find that, in their simplest version, they can improve its performance, but only modestly. We conclude that either frictions account for a tiny fraction of residual wage dispersion, or the standard model needs to be augmented to confront the data.