The distribution of group sizes in woodland baboons forms a pair of demographic oscillators that trade fertility off against predation risk. Fertility rates, however, set an upper limit on group size of around 90–95 animals. Despite this, two species of baboons (hamadryas and gelada) have groups that significantly exceed this limit, suggesting that these two species have been able to break through this fertility constraint. We suggest that they have done so by adopting a form of social substructuring that uses males as ‘hired guns’ to minimize the stresses of living in the unusually large groups required by high predation risk habitats.