The ageing of the Dutch population, resulting in an increase in the number of retirees relative to the working population, has induced a debate about the sustainability of the Dutch first pillar pension scheme (AOW). This study explores possible alternatives for the AOW. A stochastic partial equilibrium model is used to study intragenerational insurance against longevity and productivity risk. The model shows the welfare, labour-market and saving effects of a shift from a Beveridge towards a Bismarck system in which pension rights depend on labour-market history. The main conclusion is that a shift of first pillar pensions from a Beveridge towards a Bismarck system is not necessarily welfare improving from an ex-ante insurance perspective, i.e. before the veil of ignorance is lifted. Moreover, a means test of the first pillar against wealth income, which implies a lower AOW when an individual has wealth income and a lower pension premium for everyone, does not improve welfare in the setting of the model considered in this study.