The methods used for deciding the closure date for fisheries monitored by the Secretariat of CCAMLR, as described in Conservation Measures, have been difficult to implement because of the variation in catch rates shown by the fisheries. Non-fluctuating random and fluctuating random catch histories are simulated and the performance of four Models for making closure decisions is investigated under a variety of circumstances. The Model described in the existing Conservation Measures is shown to have a high probability of allowing large over- or under-shoots of the TAC. The most successful model determines the trend of catch rates using linear regression over the latest four reporting periods, and closes the fishery if these rates indicate that the TAC will be taken before the next report arrives at the Secretariat. The probability of large over-shoots of the TAC is reduced if reporting periods are small (5-days) and the reporting delay is minimal.