In 2011/2012, a French vessel conducted its first exploratory fishery for Dissostichus spp. in division 58.4.3a. A new campaign is scheduled for 2013. France has also notified its intention to participate in this exploratory fishery over the next three years in order to achieve a robust stock assessment that would provide advice on catch limits according to CCAMLR decision rules. This paper aims to present a research plan for 2013/2014 that takes into account the remarks made during the WG-FSA 2012 and to progress on modeling tools in order to improve the estimation of current biomass. An update of the assessment of Dissostichus eleginoides using a CASAL model and a simple Petersen biomass estimate derived from tagging data are presented. The CASAL model structure used for a preliminary assessment of the stock in 2012 has been retained and updated with a small number of changes to try to improve the fit of the model. B0 is estimated at around 1,400 tonnes and B2013/B0 at around 85%. Sustainable yield, calculated in accordance with the CCAMLR decision rules is around 70 tonnes for D.eleginoides whilst sustainable yield calculated from the Petersen biomass estimates and application of the gamma value (0.038 determined for toothfish in Subarea 48.4) was 21 tonnes. As further work is required to provide management advice, the catch limit of 32 tonnes for 2012/2013 is suggested.