Many nations are seeking to reform their welfare states so that costs to the government can be reduced and the quality of outcomes improved. As a potential way to achieve these aims, there has been a surge of interest in the Singaporean model which features compulsory savings accounts and transparent pricing of health services. It has achieved some of the best health-care outcomes in the world at a cost that is the lowest amongst high income countries. In this paper we show how tax cuts can be designed to help establish compulsory savings accounts so that a publicly funded welfare system can be changed into one that relies more heavily on private funding in a politically feasible way. To our knowledge, showing how both a tax and welfare reform can be jointly designed to enable this transition to occur has not been done before. Our policy reform creates institutions that have features in common with Singaporean ones, especially for health-care. However there are also key differences. We present a new unified approach to the funding of health, retirement and risk-cover (for events like unemployment) through the establishment of a set of compulsory savings accounts. A case study of New Zealand is used as an illustration. The fiscal impact of our proposed reform on the government's current and future budgets is reported, as well as its effect on low, middle and high income individuals.