The management of Champsocephalus gunnari at South Georgia is complicated by the likelihood of substantial periodic variation in natural mortality rates. These may be associated with increased consumption of icefish by Antarctic fur seals in years of poor krill availability. Thus natural mortality of icefish may, in some years, increase by a large factor (assumed here to be 4) declining to normal levels again when krill return. A scheme is elaborated that would use information from studies on krill and predators undertaken as part of CEMP to interpret or modify information from commercial fisheries and research surveys leading to estimates of stock biomass. An extension of this scheme would use predictions of coming periods of krill scarcity as early warnings of increased natural mortality on icefish. This scheme would require greater quantitative knowledge of food web dynamics within the South Georgia ecosystem than we have at present. There is therefore a need for an interim approach to setting precautionary catch limits for this fishery. An approach based on the general yield model is described, which can be used to calculate an appropriate proportion of an estimate of Bo which could be taken by fishing, under conditions where M is assumed to be highly variable from year to year.