In many countries, non-compliance with minimum wage legislation is widespread, and authorities may be seen as having turned a blind eye to a legislation that they have themselves passed. But if enforcement is imperfect, how effective can a minimum wage be? And if non-compliance is widespread, why not revise the minimum wage? This paper examines a minimum wage policy in a model with imperfect competition, imperfect enforcement and imperfect commitment, and argues that it is the combination of all three that produces results which are consistent with a wide range of stylized facts that would otherwise be difficult to explain within a single framework. We demonstrate that turning a blind eye can indeed be an equilibrium phenomenon with rational expectations subject to an ex post credibility constraint. Since credible enforcement requires in effect a credible promise to execute ex post a costly transfer of income from employers to workers, a government with an objective function giving full weight to efficiency but none to distribution is shown, paradoxically, to be unable to credibly elicit efficiency improvements via a minimum wage reform.