We analyze longitudinal cohort mortality patterns assumed to follow a broken-line regression model with binomial responses and an unknown set of joinpoints. We propose herein a simple procedure for an approximate joinpoints selection and model fitting via penalized likelihood. Whereas the method may not be as accurate as some of its more sophisticated competitors, it is computationally efficient and seems satisfactory under many simple change patterns with small-to-moderate sample sizes. In fact, the simulation study indicates that in some cases the approach may be superior to traditional sequential algorithms in identifying the correct number of change points. The estimation of the model parameters and the selection algorithms are illustrated with data on cancer mortality in a cohort of chemical workers analyzed already elsewhere using a joinpoint logistic regression approach. The results of two analyses are compared.