This paper asks what governments in the EU Member States and some US states are doing to support workers on low wages. Using model family simulations, we assess the policy measures currently in place to guarantee an adequate disposable income to working families, taking into account minimum wages, social security contributions, taxes and cash benefits. We show that despite increased efforts over the past decade, disposable incomes of certain types of minimum wage workers still fall well below the EU at-risk-of-poverty thresholds in many countries. Single earners with dependent children are especially at risk of poverty. We discuss the options for making progress.