We analyze the effect of health cost risk on optimal annuity demand and consumption/savings decisions. Many retirees are exposed to sizeable out-of-pocket medical expenses, while annuities potentially impair the ability to get liquidity to cover these costs and smooth consumption. We find that if out-of-pocket medical expenses can already be sizeable early in retirement, full annuitization is not optimal. In the other case of low health cost risk early in retirement, individuals should take advantage of the mortality credit that annuities provide and save out of the annuity income to build a buffer for health cost shocks at later ages. When comparing to empirically observed levels of annuitization, we find that high health cost risk early in retirement may resolve the annuity puzzle. Moreover, we explain the observed pattern of annuitization as a function of initial wealth at retirement. For personal financial planning purposes, we develop a simple rule of thumb for annuity demand, based on expected health cost risk early in retirement, wealth at retirement, and minimum consumption levels. We show that the welfare costs from using the rule compared to the full life cycle model are small.