This paper investigates some problems with the Colorado Plateau uranium miners cohort when fitting the mechanistic model of carcinogenesis of Moolgavkar et al. (MVK model) to nested case-control data for lung cancers. The influence of data for hard rock mining and work histories on the model fitting is examined and found to be highly influential. The question of selecting the most appropriate number of controls per case is also considered. Analyses were carried out assuming that the hard rock mining exposure occurred prior to all other work histories and that miners received no exposure between work histories. The use of less than 15 controls per case was found to seriously restrict the quality of fit of the models. The best fitting, most reliable model contained linear effects of radon exposure on the first mutation rate, the rate of differentiation, and the rate of death of the intermediate cells. An effect of smoking on the growth of the intermediate cells was also included in the model. It is concluded that owing to the complexity of the MVK model and the limited amount of information in this dataset, the reliability of the Colorado Plateau dataset for fitting this type of model, particularly in a case-control format, is questionable.