Although annuities provide longevity insurance that should, in theory, be attractive to risk-averse households facing an uncertain lifespan, rates of voluntary annuitization remain extremely low. We evaluate a proposed annuity product, the Advanced Life Deferred Annuity, an annuity purchased at retirement, providing an income commencing in advanced old age. Using numerical optimization techniques, we show that this product would provide a substantial proportion of the longevity insurance provided by an immediate annuity, at a small fraction of the cost. At plausible levels of actuarial unfairness, households should prefer it to both immediate and postponed annuitization, and an optimal decumulation of unannuitized wealth. We show that few households would suffer significant losses were it used as a 401(k) plan default.