We consider an economy with a tax on all labor earnings. We discover that a slightly binding minimum wage on one sector can enhance efficiency. The minimum wage attracts high‐reservation wage workers into the minimum‐wage sector. If the labor demand curve in the free sector is quite flat, the vast majority of workers displaced by the minimum wage find employment in the free sector, raising aggregate employment. This displacement of workers by the only slightly binding minimum wage has negligible effects on efficiency. So efficiency and tax revenue rise as the minimum wage pulls labor out of untaxed leisure, where too much of the labor force is lurking, into taxed work.