Economic inequality in contemporary advanced societies is strongly tied to the variation in wages across occupations. We examine the extent to which this variation is captured by social class and occupational prestige and ask how the associations between class, prestige, and wages can be explained. On the basis of data from 11 countries in the European Social Survey (ESS) 2004, we find (a) that class and prestige account for a very large proportion of the occupational variation in wages; (b) that the tight links between class, prestige, and wages are strongly associated with the skill requirements of jobs but only weakly tied to other positional traits, including authority, autonomy, and scarcity; and (c) that these findings are highly similar in all countries examined. We conclude that the rank order of positions in the labor market is a social constant driven by efficiency requirements of work organizations rather than by the exercise of power. This iron law of labor market inequality clearly contradicts major class theoretical models, including Wright's and Goldthorpe's. In addition to empirically refuting contemporary class theory, we offer a number of more conceptual arguments to the same effect. At a macro level, however, power relations arguably affect the rate of economic inequality by determining the reward distance between positions in the constant rank order, as indicated by the large cross-national variation in wage dispersion.