The expected increase of 3D data which will result from the development of multimedia systems requires improved compression algorithms in order to reduce the cost of data transmission. In the case of 3D data represented by 3D meshes, the coding procedure involves three different coding steps for the topology, the geometry and the attributes (such as texture, color and curvature) of the mesh. In this paper, we address the issue of 3D mesh geometry coding. Within a predictive framework and under a bitrate control constraint, we study two different prediction rules, namely the parallelogram and the polygonal rule, and present a comparison of their performances. The parallelogram rule uses the ancestors defined by the triangle tree traversal order of the mesh to predict the current vertex, while the polygonal rule performs the prediction from the already decoded vertices in the polygons incident to the current vertex. The two prediction rules applied to polygonal and triangular meshes lead to different behaviors in terms of compression ratio and distortion index. The parallelogram rule yields better results in the case of triangular models, while the polygonal rule is more efficient for most of the polygonal models. Based on this analysis, we combine the two prediction rules into a novel scheme, taking advantage of the specificity of each prediction. The simulations, carried out on 294 models of the Moving Picture Expert Group (MPEG) data set, established that an effective gain of up to 50% reduction of the distortion at a given bitrate was obtained by using the cooperative scheme.