Reproductive skew in multimale groups may be determined by the need for alpha males to offer reproductive opportunities as staying incentives to subordinate males (concessions), by the relative fighting ability of the alpha male (tug-of-war) or by how easily females can be monopolized (priority-of-access). These models have rarely been investigated in species with exceptionally long male tenures, such as white-faced capuchins, where female mate choice for novel unrelated males may be important in shaping reproductive skew. We investigated reproductive skew in white-faced capuchins at Sector Santa Rosa, Costa Rica, using 20 years of demographic, behavioural and genetic data. Infant survival and alpha male reproductive success were highest in small multimale groups, which suggests that the presence of subordinate males can be beneficial to the alpha male, in line with the concession model’s assumptions. None of the skew models predicted the observed degree of reproductive sharing, and the probability of an alpha male producing offspring was not affected by his relatedness to subordinate males, whether he resided with older subordinate males, whether he was prime aged, the number of males or females in the group or the number of infants conceived within the same month. Instead, the alpha male’s probability of producing offspring decreased when he was the sire of the mother, was weak and lacked a well-established position and had a longer tenure. Because our data best supported the inbreeding avoidance hypothesis and female choice for strong novel mates, these hypotheses should be taken into account in future skew models.