We show that a new, simple, and robust general mechanism for the social suppression of within-group selfishness follows from Hamilton's rule applied in a multilevel selection approach to asymmetrical, two-person groups: If it pays a group member to behave selfishly (i.e., increase its share of the group's reproduction, at the expense of group productivity), then its partner will virtually always be favored to provide a reproductive "bribe" sufficient to remove the incentive for the selfish behavior. The magnitude of the bribe will vary directly with the number of offspring (or other close kin) potentially gained by the selfish individual and inversely with both the relatedness r between the interactants and the loss in group productivity because of selfishness. This bribe principle greatly extends the scope for cooperation within groups. Reproductive bribing is more likely to be favored over social policing for dominants rather than subordinates and as intragroup relatedness increases. Finally, analysis of the difference between the group optimum for an individual's behavior and the individual's inclusive fitness optimum reveals a paradoxical feedback loop by which bribing and policing, while nullifying particular selfish acts, automatically widen the separation of individual and group optima for other behaviors (i.e., resolution of one conflict intensifies others).