We develop a model of a multiple-species, stochastic harvesting technology. We examine harvesting behavior, at-sea discards and economic performance under various quota balancing mechanisms -- provisions intended to help fishermen match random catches with quota holdings -- in a multiple species fishery. We show that regulations that allow frictionless quota trading reduce at at-sea discards and increase economic performance. Regulations that offer fishermen flexibility to choose the mix of species landed do not eliminate discards, and can create unintended management problems. Our results provide new insights for improving the design quota-managed fisheries.