In this work we present a novel surplus production model for fisheries stock assessment. Our goal is to enhance parameter estimation and fitting speed. The model employs a production function that differs from the canonical logistic (Schaefer) and Gompertz (Fox) functions, but is still connected to the Pella-Tomlinson formulation. We embed this function in a state-space model, using observed catch-per-unit-effort indices and measures of fishing effort as input. From the literature we derive Bayesian prior densities for all model hyperparameters (carrying capacity, catchability, growth rate and error variance), as well as the state (annual stock biomass). We use the well-studied Namibian hake fishery as a case study, via which we compare the Schaefer, Fox and Pella-Tomlinson models with the new model. We also develop a package for the software R, which employs a Shiny application for data exploration, model specification, and output analyses. Posterior densities of hyperparameters and reference points agree across models. Identifiability issues emerge in the more cumbersome Pella-Tomlinson model. The new model yields small but consistent improvements in precision. It also renders implementation faster and easier, with no hidden truncation of negative biomasses. We conclude by discussing theoretical and practical extensions to this new model.