The catch from bottom longline stations sampled from a series of research cruises around Lanzarote and Fuerteventura (Canary Islands, NE Atlantic) was analysed in terms of fish distribution, density and diversity. The distribution of the number of species and individuals caught per station appeared to fit well the Poisson and Exponential distribution function, respectively. In particular, the parameter of the Poisson’s distribution appeared to provide an index of the point (at station scale) diversity, and its confidence interval, allowing for statistical comparisons. The relationships between point diversity, the alpha diversity (in the depth strata) and the beta diversity (along the depth gradient) were investigated. Around the islands, the density and the point diversity of the predator fish declined with depth down to about 800 m and then increased in the deeper stratum. The alpha diversity was the lowest in the deeper stratum but the taxonomic distinctness was similar to that of shallower strata. The beta diversity showed some faunal breaks along the depth gradient. The carnivorous fish fauna can be understood as comprised of three major assemblages: shelf, upper slope and mid-slope that are different both in terms of species composition and point, alpha and beta diversities. The relevance of this simple method for ecological studies of fish assemblage in the context of non-trawlable grounds is discussed, in particular for the slope and other areas of established or developing deep-water fisheries.