The decomposition of 3D shapes into simple yet representative components is a very intriguing topic in computer vision as it is very useful for many possible applications. Superquadrics may be used with benefit to obtain an implicit representation of the 3D shapes, as they allow to represent a wide range of possible forms by few parameters. However, in the computation of the shape representation, there is often an intricate trade-off between the variation of the represented geometric forms and the accuracy in such implicit approaches. In this paper, we propose an improved loss function, and we introduce beneficial computational techniques. By comparing results obtained by our new technique to the baseline method, we demonstrate that our results are more reliable and accurate, as well as much faster to obtain.