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This study focuses on the statistical description and analysis of road surface irregularities that are essential for heavy-vehicle fatigue assessment. Three new road profile models are proposed: a homogenous Laplace moving average process, a non-homogenous Laplace process and a hybrid model that combines Gaussian and Laplace modelling. These are compared with the classical homogenous Gaussian process as well as with the non-homogenous Gaussian model that represents the road surface as a homogenous Gaussian process with Motor Industry Research Association spectrum enhanced by randomly placed and shaped irregularities. The five models are fitted to eight measured road surfaces and their accuracy and efficiency are discussed.