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We derive a method for interpreting information about the reproductive performance of mothers of a sample of informants and apply it to the history of low fertility among the !Kung of the Kalahari desert of southern Africa. The method formalizes the commonsense procedure of weighting mothers with 1 birth by 1, with 2 births by 1/2, with 3 births by 1/3, etc. An expression for the confidence interval of the estimate of mean completed fertility of fertile women in the mothers’ cohort is given. Several independent studies show that !Kung women have low fertility, with a population average completed family size of slightly over 4. Our method, applied to the cohort of old informants, shows that fertility is comparable among !Kung women, mothers of old informants, who were born in the late nineteenth and early twentieth centuries. If the cause is an endemic infectious disease of long standing in this region, there are important implications for the history of southern and central Africa.