The problem of recovering the shape of objects from three-dimensional data is important to many areas of computer graphics and vision. We present here a method for the recovery of single-part objects from unstructured 3D points sets, based on the fitting of deformable superquadric models. The limitations of least-squares minimisation as a technique for fitting superquadric models are discussed. After investigating the possibility of using a genetic algorithm as an alternative, we propose a hybrid approach to the recovery of deformable superquadrics based on a two-stage fitting process that combines a genetic algorithm and nonlinear least-squares minimisation.