The Leslie depletion model has been used to examine local patterns in catch per unit effort (CPUE) in the longline fisheries for Patagonian toothfish (Dissostichus eleginoides) around South Georgia and the Pacific coast of Chile. This paper presents a re-working and synthesis of previous analyses to examine whether declines in CPUE can be modelled using a linear regression of catch per hook against cumulative catch, when single vessels operate in localised areas for periods of at least three days. The results suggest that there is greater potential for application of the model in some areas than in others, but in general there is no sufficiently consistent signal in the data for the depletion model to be used to estimate local abundance. A number of possible explanations are considered, including movements of fish, the behaviour of fishermen, variable catchability and insufficiently high catch to cause local depletion. Suggestions are made for further work.