Social queues, in which subordinates wait for their turn to inherit dominant breeding status, are a familiar feature of many animal societies. However, little is known about the mechanisms stabilizing social queues given the inevitable conflict over rank between group members. Here, we report the role of punishment and cooperation in promoting the stability of size-based queues in a coral-dwelling goby, Paragobiodon xanthosomus (Gobiidae). Quantitative analysis of the size-structure of queues revealed that individuals of adjacent rank differ in size by a specific size ratio, and comparisons of individual growth rates within queues demonstrated that specific size ratios are maintained over time via the regulation of subordinate growth rates. Furthermore, contest experiments demonstrated that the specific size ratio represents a threshold above which the subordinates become a threat to their immediate dominant, and as a result, dominants evict subordinates that exceed this size ratio from the group. We propose that threshold size ratios are maintained by subordinates as a form of peaceful cooperation whereby they avoid inflicting costs on dominants, and that such cooperation arises in response to the threat of punishment in the form of eviction by dominants. Societal stability is therefore achieved through the effects of punishment and cooperation acting in concert to promote the resolution of conflict over rank between group members.