Wilcox (1981a) proposed a model for an answer‐until‐correct scoring procedure that solves various measurement problems. The purpose of this paper is to check empirically an implication of the model, and to propose and investigate some strong true‐score models. One of the strong true‐score models assumes the probability of guessing the correct response to an item is a strictly increasing function of an examinee's ability level, and the model gives a reasonable fit to the data. The paper illustrates that this new model is easily applied to situations where the beta‐binomial model is typically used. The other models, including the Dirichlet‐multinomial model, proved to be unsatisfactory. Finally, potential difficulties with the new model are discussed, and possible directions for future research ar