This work introduces a new compression scheme for point sets. This scheme relies on an adaptive binary space partition (BSP) which takes into account the geometric structure of the point set. This choice introduces geometrical rather than combinatorial information in the compression scheme. In order to effectively improve the final compression ratio, this partition is encoded in a progressive manner, decreasing the number of bits used for the quantisation at each subdivision. This strategy distributes the extra cost of the geometry encoding onto the maximal number of points, compressing in average 15% more than previous techniques.