The Age-Structured Production Model (ASPM) presented to previous meetings is refined to allow the estimation of a selectivity-at-age function that decreases at larger ages. This is, in particular, to accommodate the view of the August 2003 meeting of the Subgroup on assessment methods that 0.2 yr-1 is likely the largest value of natural mortality M that is plausible for toothfish. Catch, catch-at-length and GLM standardised CPUE data are all extended for one further year. Despite model refinements, the CPUE data and catch-at-length data remain sharply inconsistent within the modelling framework considered. The former suggests the resource to be heavily depleted, whereas the latter suggests quite the reverse. Priority areas for further investigation to attempt to resolve this inconsistency are suggested. In the meantime, based upon a cautious interpretation of projections over the wide range of current stock status that can be argued from these analyses, it is suggested that annual catch levels should not exceed a few hundred tonnes.