Catch-per-unit-effort (CPUE) provides one of the most commonly used abundance indices in fishery research. The literature, however, offers no unique method of estimating CPUE and its variance from catch and effort data. In this paper we develop two models (univariate and bivariate) that generalize previous approaches and remain valid under management restrictions on catch and/or effort. Both models estimate CPUE from measures of central tendency in the underlying catch and effort distributions. The models involve normalizing transformation parameters that, along with other parameters, are estimated by maximum likelihood. We illustrate the models using data from Pacific ocean perch (Sebastes alutus). For the four data sets examined, the univariate and bivariate models result in similar estimates of CPUE. However, other commonly used CPUE measures lead to inconsistent results, in particular for data sets in which catch was restricted by low trip limits. We recommend the bivariate model, since it accounts for the bivariate structure of catch and effort data. Furthermore, it can easily be adapted to accommodate alternative indices, for example, the effort required to attain a specified catch.