Catch per unit effort (CPUE) is often assumed to be an index of stock abundance. Here we present an experiment and a general model for testing this assumption. We used the submersible Pisces IV to make visual estimates of reef-fish density in the Strait of Georgia, British Columbia. These density estimates were compared with CPUE estimates obtained by research angling at the same sites. Our model allows for no relationship between CPUE and density, strict proportionality, and departures from proportionality at either low or high densities or both. We performed the analysis using an ordinary least squares (OLS) model and an errors-in-variables (EV) model that includes error in both CPUE and density. For the dominant species (quillback rockfish, Sebastes maliger), the relationship was one of strict proportionality. However, CPUE was a poor abundance index when data were combined across species. In these cases the OLS and EV models generally resulted in different conclusions; the EV model explained a low CPUE at high density by allowing for error in the density measurement.