We develop and simulate a stochastic lifecycle model to investigate optimal annuity purchases at retirement. Retirees can invest in risky assets, purchase fairly priced immediate or deferred lifetime annuities, and are eligible for a targeted safety net pension. We match baseline parameters to current Australian settings and conduct scenario analyses over a wide range of individual preferences and financial market outcomes. Except where individuals need to insure a consumption floor, both immediate and deferred annuity purchases are largely crowded out by the means‐tested public pension. Welfare losses caused by zero annuitisation are small compared with the losses caused by completely annuitising all savings, particularly if wealth at retirement is low. Decumulation policy should ensure individuals are well informed of the insurance value of annuities and accommodate diverse choices.