Abstract: In this paper, we propose a novel progressive lossless mesh compression algorithm based on Incremental Parametric Refinement, where the connectivity is uncontrolled in a first step, yielding visually pleasing meshes at each resolution level while saving connectivity information compared to previous approaches. The algorithm starts with a coarse version of the original mesh, which is further refined by means of a novel refinement scheme. The mesh refinement is driven by a geometric criterion, in spirit with surface reconstruction algorithms, aiming at generating uniform meshes. The vertices coordinates are also quantized and transmitted in a progressive way, following a geometric criterion, efficiently allocating the bit budget. With this assumption, the generated intermediate meshes tend to exhibit a uniform sampling. The potential discrepancy between the resulting connectivity and the original one is corrected at the end of the algorithm. We provide a proof-of-concept implementation, yielding very competitive results compared to previous works in terms of rate/distortion trade-off.