A model incorporating 5-year age groups, single-year period effects, and 5-year cohort effects is fitted by Poisson regression to breast and cervical cancer incidence from New South Wales, Australia, over 20 years. The lack of identifiability of the parameters in the model is dealt with by end-point smoothing of the cohort effects. The model is fitted separately to incidence rates for each cancers, and is used, together with some minimal subject-matter assumptions, to make projections.