In many countries, the authorities turn a blind eye to minimum wage laws that they have themselves passed. But if they are not going to enforce a minimum wage, why have one? Or if a high minimum wage is not going to be enforced one hundred percent, why not have a lower one in the first place? Can economists make sense of such phenomena? This paper argues that we can, if a high official minimum wage acts as a credible signal of commitment to stronger enforcement of minimum wage laws. We demonstrate this as an equilibrium phenomenon in a model of a monopsonistic labor market in which enforcement is costly, and the government cannot pre-commit to enforcement intensity. In this setting we also demonstrate the paradoxical result that a government whose objective function gives greater weight to efficiency relative to distributional concerns may end up with an outcome that is less efficient. We conclude by suggesting that the explanations offered in this paper may apply to a broad range of phenomena where regulations are imperfectly enforced.