This paper assesses the potential for the commercial trawl fisheries in the Heard Island area (Statistical Division 58.5.2) to significantly affect, in the long term, spawning biomass of three taxa caught as by-catch: Channichthys rhinoceratus, Lepidonotothen squamifrons and Bathyraja spp. (deep-water skates). The long-term annual yield for each of the three taxa was estimated using the generalised yield model (GYM) used by the CCAMLR Working Group on Fish Stock Assessment (WG-FSA). Input data included biomass estimates from surveys in the region from 1990 to 1993 and a limited amount of biological data from the local area. Where possible, values for missing input parameters were obtained from the literature, for the same species from other areas, otherwise proximate data for similar species elsewhere in the world were used. The second part of the analysis examined the amount of each species caught during commercial operations and the effectiveness of by-catch provisions (the 5% rule) set by CCAMLR in 1996 to ensure that the status of these commercial species is not affected by these commercial fisheries. The ranges of estimates of long-term annual yields for C. rhinoceratus, L. sqamifrons and skates were 62 to 87 tonnes, 7 to 911 tonnes and 50 to 210 tonnes respectively. While refinement of these estimates is needed, they enable a preliminary examination of the potential for the fishery to be exceeding long-term sustainable annual yields. For C. rhinoceratus, L. squamifrons and skates (principally B. eatoni), the total by-catch during commercial activities in 1996/97 was approximately 5%, 58% and 11% of the respective lowest estimates of yield. These results indicate that the current commercial trawl fisheries around Heard Island are unlikely to be negatively affecting these stocks. Notably, by-catch species appeared as a high proportion of the catch (greater than 5%) when only small amounts of fish were caught (less than 100 kg of by-catch), which was usually during prospecting. By-catch was usually very low as a proportion of the total catch when large catches of target species were taken, indicating that CCAMLR's 1996 by-catch rules need revising in order that prospecting may be undertaken. Thus, to enable prospecting for commercial aggregations of Champsocephalus gunnari or Dissostichus eleginoides while protecting the by-catch species from excessive fishing effort, the rules governing by-catch for the Heard Island area could be a combination of (i) limiting the total by-catch in a year to the estimates of long-term annual yield, (ii) allowing catches of by-catch species of up to 100 kg in any one haul and (iii) changing fishing grounds if the catch of any one of the by-catch species exceeds 100 kg and the total by-catch is greater than 5% of the total catch in a single haul.