In this paper we present a simple technique to approximate the volume enclosed by a given triangle mesh with a set of overlapping ellipsoids. This type of geometry representation allows us to approximately reconstruct 3D-shapes from a very small amount of information being transmitted. The two central questions that we address are: how can we compute optimal fitting ellipsoids that lie in the interior of a given triangle mesh and how do we select the most significant (least redundant) subset from a huge number of candidate ellipsoids. Our major motivation for computing ellipsoid decompositions is the robust transmission of geometric objects where the receiver can reconstruct the 3D-shape even if part of the data gets lost during transmission.