Do minimum wages reduce in-work-poverty and wage inequality? Or can alternative policies do better? We evaluate theses issues for the exemplary case of Germany that suffers from high unemployment among low-skilled workers and rising wage dispersion at the bottom of the wage distribution. We analyze the impact of three different policy options, currently discussed in Germany, on employment, wage inequality, public expenditures, and incomes of poor households: 1) a statutory minimum wage, 2) a combination of minimum wages and wage subsidies as e.g. in France and the Netherlands, and 3) pure wage subsidies to low-paid workers. We find that a minimum wage of EUR 7.50 would cost 840,000 low-paid jobs and increase the fiscal burden by about EUR 4 billion per year, while poor households’ income rises only by EUR 1.1 billion per year. With pure wage subsidies, the government can ensure more favorable employment and income effects. Combining a minimum wage with a wage subsidy turns out to be extremely costly and inferior to wage subsidies in all respects. JEL Code: H2, I3, J3.