We examine two alternatives to the survey recruitment/GY method for estimating toothfish abundance. An age structured production model (ASPM) is constructed and tuned to the CPUE series. The fit of the model to the CPUE series is not good, and there are several unexplained problems. The first is that the CPUE in the early 1990s did not decline as would be expected as the resource was initially fished quite heavily. The second is that when a decline was seen, it was much more abrupt than would be predicted by the model. Thirdly, all models predict a continuing decline, not the increase in CPUE that actually has been seen since 1996. Fitting the model to partial CPUE series, or assuming an unknown additional level of IUU fishing, improves the fit of the model but does not fully explain the initial lack of early decline, the abrupt decline between 1995 and 1996 and the subsequent increase in CPUE. Toothfish have been tagged at South Georgia since 2000, and it is possible now to examine the usefulness of tagging data to estimate population size. We use two equations, the Jolly-Seber unbiased method and a simple M- and tagging mortality adjusted Petersen estimator. This latter analysis suggests biomass in 2002 was between 78,000 and 114,000 t.