Focusing on a seller's regret in not acting optimally, we develop a model of overbooking and fare-class allocation in the multifare, single-resource problem in revenue management. We derive optimal static overbooking levels and booking limits, in closed form, that minimize the maximum relative regret (i.e., maximize competitive ratio). We prove that the optimal booking limits are nested. Our work addresses a number of important issues. (i) We use partial information, which is critical because of the difficulty in forecasting fare-class demand. Demand and no-shows are characterized using interval uncertainty in our model. (ii) We make joint overbooking and fare-class allocation decisions. (iii) We obtain conservative but practical overbooking levels that improve the service quality without sacrificing profits. Using computational experiments, we benchmark our methods to existing ones and show that our model leads to effective, consistent, and robust decisions.