To develop a model to estimate the degree of unobserved heterogeneity in morality risks in a population, it is necessary to specify two types of functions, one describing the age-specific rate of increase of mortality risks for individuals and the other describing the distribution of mortality risks across individuals. There has been considerable interest in the question of how sensitive the estimates of heterogeneity are to the choices of these functions. To explore this question, high-quality data were obtained from published Medicare mortality rates for the period 1968–1978 for analysis of total mortality among the aged. In addition, national vital statistics data for the period 1950–1977 were used to analyze adult lung cancer mortality. For these data, the estimates of structural parameters were less sensitive to reasonable choices of the heterogeneity distribution (gamma vs. inverse Gaussian) than to reasonable choices of the hazard rate function (Gompertz vs. Weibull).