The paper deals with the effect of a lowered speed limit on the number of accidents in which there are fatalities, injuries and vehicle damage on Swedish motorways. Two models extending the Poisson and negative binomial count data models are used for estimation. The extended models account for both overdispersion and potential dependence between successive counts. The inferences of the parameters depend on the assumed form of overdispersion. It is found that the speed limit reduction has decreased the number of accidents involving minor injuries and vehicle damage. Furthermore, the models allowing for serial correlation are shown to have the best ex ante forecasting performance.