Hierarchical mesh representation and mesh simplification have been addressed in computer graphics for adaptive level-of-detail rendering of 3D objects. In this paper, by using a new simplification method to design hierarchical 3D meshes such that each mesh level has Delaunay topology, we can obtain not only meshes with desired geometric properties, but also efficient compression of the mesh data. The hierarchical compression technique is based on a nearest-neighbor ordering of mesh node points. The baseline is the use of entropy coding of linear prediction between nearest neighbor node coordinates. Vector quantization is also employed just to be able to process efficiently statistical dependences between prediction error vectors of a node. The compression method allows progressive transmission and quality scalability.