It is of considerable interest to forecast future mesothelioma mortality. No measures for exposure are available so it is not straightforward to apply a dose–response model. It is proposed to model the counts of deaths directly by using a Poisson regression with an age–period–cohort structure, but without offset. Traditionally the age–period–cohort is viewed as suffering from an identification problem. It is shown how to reparameterize the model in terms of freely varying parameters, to avoid this problem. It is shown how to conduct inference and how to construct distribution forecasts.