In this paper we explore the implication of a morbidity risk for the relationship between longevity and annuitization. We divide old-age life into two periods with uncertain survival from the end of the first to the end of the second. We show that a rise in the survival rate causes different patterns of change in annuitization, depending on the initial survival rate. When the initial survival rate is low (high), there is full (partial) annuitization. There is thus an inverse relationship between longevity and annuitization.