This paper presents, discusses and tests a generalized Random Regret Minimization (G-RRM) model. The G-RRM model is created by replacing a fixed constant in the attribute-specific regret functions of the RRM model, by a regret-weight variable. Depending on the value of the regretweights, the G-RRM model generates predictions that equal those of, respectively, the canonical linear-in-parameters Random Utility Maximization (RUM) model, the conventional Random Regret Minimization (RRM) model, and hybrid RUM-RRM specifications. When the regretweight variable is written as a binary logit function, the G-RRM model can be estimated on choice data using conventional software packages. As an empirical proof of concept, the G-RRM model is estimated on a stated route choice dataset, and its outcomes are compared with RUM and RRM counterparts.