Choosing economically optimal health insurance coverage involves a tradeoff between risk reduction and the overuse of health care. The economic purpose of insurance is to reduce financial uncertainty or risk--the more health insurance lowers the risk, the greater will be the increase in social well-being. But increases in health insurance also increase the amount of medical care demand, because insurance lowers the out-of-pocket cost of health care--the larger the demand response of medical care to cost sharing, the greater the decrease in social well-being, due to the purchase of too much health care. This report examines this tradeoff empirically by estimating both the demand for health insurance and the demand for health services. It relies on data from a randomized controlled trial of cost sharing's effects on the use of health services and on the health status for a general, nonelderly (under age 65) population. The results suggest that the optimal coinsurance rate (percentage of the health care bill paid directly by patients) should be about 50 percent. Although this estimate is higher than the 30 percent now paid out of pocket, the estimated economic loss from the discrepancy is quite modest. However, there is a substantial economic loss for up to 40 million Americans resulting from the lack of insurance.