In this brief, we examine how Social Security proposals could eliminate poverty and relative poverty (defined as having low income relative to average wages in the economy) for older adults and people who receive Social Security Disability Insurance benefits. We add a basic minimum benefit to three prominent Social Security proposals that as currently designed would increase or maintain relative poverty over time.  The additional cost is moderate enough that any of these proposals could be adjusted to virtually eliminate poverty and still provide significantly higher real benefits across the board for future generations of retirees and disabled workers.