The unusually long lifespans of humans and the persistence of post-reproductive lifespans in women represent evolutionary puzzles because natural selection cannot directly favour continued living in post-menopausal women or elderly men. Suggested sources of indirect selection require genetic correlations between fitness and survival or reproduction at younger ages, reproduction in the opposite sex, or late-life contributions to offspring or grandoffspring fitness. Here we apply quantitative genetic analyses to data from a historical human population to explicitly test these evolutionary genetic hypotheses. Total genetic selection increased the male post-50 lifespans by 0.138 years per generation; 94% of this arose from indirect selection acting to favour early-life fitness in both sexes. These results argue strongly against life-history models of ageing that depend on trade-offs between reproduction and late-life survival. No source of indirect selection for female post-50 lifespan was detected, deepening the mystery of why female post-reproductive survival persists. This result is probably due to recent changes in the genetic architecture of female lifespan, and it highlights the need for similar quantitative genetic analyses of human populations at other points along demographic transitions.