This paper analyses the trade-off between the incentive effects of increased uncertainty and the welfare benefits of risk-sharing in the design of optimal tax schedules. We use numerical methods to characterise the tax schedule and to give comparative static results of changing risk aversion, uncertainty and the cost of effort. Increased uncertainty may increase effort for precautionary reasons, but leads to greater risk sharing in the optimal tax schedule. Similarly, a reduced cost of effort leads to greater risk sharing. Incentives to work are induced through punishment at low output realisations if risk aversion is high, and through reward of high output if risk aversion is low. We also consider introducing extra randomisation into the rax schedule to further incentivise individuals. This is only optimal if the form of the tax schedule is constrained, for example to be linear.