Older wealth holders spend down assets much more slowly than predicted by classic life-cycle models. This paper introduces health-dependent utility into a model with incomplete markets in which preferences for bequests, expenditures when in need of long-term care, and ordinary consumption combine with health and longevity uncertainty to explain saving behavior. To sharply identify motives, it develops strategic survey questions (SSQs) that elicit stated preferences. The model is estimated using these SSQs and wealth data from the Vanguard Research Initiative. The desire to self-insure against long-term-care risk explains a substantial fraction of the wealth holding of many older Americans.