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A new method is introduced for the lossy compression of a LAS file. LAS files store the results from LiDAR scanning, and contain a huge amount of points with associated scalar values. The proposed method consists of four steps: eliminating those points within the oversampled regions, moving the position of the remaining points within the user-specified limits, variable-length coding, and arithmetic compression. This method was compared with the only known lossy LAS files compression method, as owned by LizardTech™. As shown by experimentation, the proposed method is considerably better than the referenced method.