The concept of ‘Maximum Sustainable Yield’ (MSY) has provided a useful guideline for resource management under the assumptions of a simple population model and simple objectives. This paper explores different guidelines under more realistic population models, taking account of the objectives set out in Article II of the CCAMLR Convention. The criteria will depend on whether the main concern is with recruitment or growth overfishing. Account also needs to be taken of the uncertainties associated with any assessment. Suggestions are made for the provision of advice to the Commission for the finfish and krill fisheries.