A doubly stochastic switching model previously used by the author to check against doubly stochastic ‘white-noise' models is generalized in the case of Poisson processes to any distribution of fluctuating intensity rates. The resulting Cox process is used in place of a simple Poisson process as the basis of a mixed model, which is then fitted to some data on automobile accidents previously analysed by Seal (1980) in terms of a mixed Poisson process. It is shown that there is just significant evidence in favour of some additional heterogeneity ‘within' each year for individual drivers; the nature of the data analysed (yearly time intervals) does not, however, allow discrimination between heterogeneity which is definitely attributable to a common fluctuating environment, and that which is in effect independent for each driver.