We present a surface compression ethod that stores surfaces as wavelet-compressed signed-distance volumes. Our approach enables the representation of surfaces with complex topology and arbitrary numbers of components within a single multiresolution data structure. This data structure elegantly handles topological modification at high compression rates. Our method does not require the costly and sometimes infeasible base mesh construction step required by subdivision surface approaches. We present several improvements over previous attempts at compressing signed-distance functions, including an O(n) distance transfor, a zero set initialization method for triangle meshes, and a specialized thresholding algorithm. We demonstrate the potential of sampled distance volumes for surface compression and progressive reconstruction for complex high genus surfaces.