After a short revue of the resolution of few body problems with the hyperspherical harmonics formalism, we develop a method to generate an “optimal subset” of basis functions that approximate the exact wavefunction up to third order of perturbations. Examples are given for three-body systems, with emphasis on the hypertriton. In this latter case, numerical results show that our optimal subset gives an energy some 40 keV higher than that found using a complete set of hyperspherical harmonics.