Longevity risk is a problem for older people worldwide. The majority of people worldwide age 75 and older do not receive social security old-age benefits. This problem mainly occurs in lower-income countries. This paper argues for old-age benefits coverage for persons age 75 and older through longevity insurance benefit programmes. Because of the advanced age at which these programmes start paying benefits, such a goal would be relatively inexpensive for most countries. This would be an intermediate goal toward full coverage of all older persons. This paper discusses the Care Allowance in Poland for persons age 75 and older and the Age 80 Allowance in Ireland as models that can be adapted to lower-income and moderate-income countries with low coverage rates for extending pension coverage to people starting at an advanced age.