We consider an economy (e.g., Chile 1973-83 or modern Turkey) with a minimum wage sector and a free sector, and a tax on labor earnings. We ask "Can a slightly binding minimum wage simultaneously raise tax revenue, employment, and economic efficiency?" We answer "Yes, if the elasticity of demand for labor in the minimum-wage sector exceeds the elasticity of demand in the free sector." The logical key is that the minimum wage draws high reservation-wage workers into the labor force, who give up untaxed leisure in exchange for taxed work and thereby increase revenue, employment and efficiency.