We introduce a method for modelling insurance claim sizes, including zero claims. A mixed discrete-continuous model, with a probability mass at zero and an Inverse Gaussian continuous component, is used. The Inverse Gaussian distribution accommodates the extreme right skewness of the claim distribution. The model explicitly speci¯es a logit-linear model for the occurrence of a claim; and log-linear models for the mean claim size (given a claim has occurred); and the dispersion of claim sizes (given a claim has occurred). The method is illustrated on aa Australian motor vehicle insurance data set.