In this paper we introduce a composite Exponential-Pareto model, which equals an exponential density up to a certain threshold value, and a two parameter Pareto density for the rest of the model. Compared with the exponential, the resulting density has a similar shape and a larger tail. This is why we expect that such a model will be a better fit than the exponential one for some heavy tailed insurance claims data (e.g. with extreme values). Subject Classification: 60E05, 62F10.