This paper analyses optimal income taxation as a trade-off between the incentive effects of increased uncertainty and the welfare benefits of social insurance. Greater prudence increases labour supply because of precautionary incentive effects which reduce the progressivity of the optimal income tax schedule. Increased uncertainty increases progressivity of the income tax schedule because of a greater value of social insurance. Optimal tax progressivity depends on the ratio of prudence to risk aversion: when this ratio is high, incentive effects dominate the social insurance effect, leading to declining optimal income tax rates.