The strategic objectives for fisheries, which are enshrined in international conventions, are to maintain or restore stocks to produce maximum sustainable yield (MSY) and to implement the ecosystem approach, requiring that interactions between species be taken into account and conservation constraints be respected. While the yield and conservation aims are, to some extent, compatible when a fishery for a single species is considered, species interactions entail that MSY for a species depends on the species with which it interacts, and the yield and conservation objectives therefore conflict when an ecosystem approach to fisheries management is required. We applied a conceptual size‐ and trait‐based model to clarify and resolve these issues by determining the fishing pattern that maximizes the total yield of an entire fish community in terms of catch biomass or economic rent under acceptable conservation constraints. Our results indicate that the eradication of large, predatory fish species results in a potential maximum catch at least twice as high as if conservation constraints are imposed. However, such a large catch could only be achieved at a cost of forgone rent; maximum rent extracts less than half of the potential maximum catch mass. When a conservation constraint is applied, catch can be maximized at negligible cost in forgone rent, compared with maximizing rent. Maximization of rent is the objective that comes closest to respecting conservation concerns.