It has been recognized for some time that the risk of producing maleless clutches should select for a lower than binomial variance in the sex ratio of organisms with female–biased sex ratios, small clutches and breeding groups containing the clutch of a single female. However, to date, precise sex ratios have only been reported for organisms with haplodiploid sex determination, a system which allows direct control of the sex of individual offspring. In contrast, under heterogametic sex determination chance is expected to play a crucial role in determining the sex composition of any one family, in particular when males are the heterogametic sex. Here, we present evidence of precise or underdispersed primary sex ratios in the Neotropical social spider Anelosimus domingo Levi. We show that this diplodiploid species with male heterogamety has not only beaten the odds of meiosis by producing mostly daughters, but has also attained relative precision in the proportion of sons and daughters produced in any one clutch. The latter finding suggests the existence of mechanisms that allow sorting of the two types of sperm in this spider species.