The use of overcomplete expansion basis functions can be useful for reproducing important details of the structure of a few-particle system by a relatively small number of basis functions. The case considered in this paper is the hyperspherical harmonic basis which is complete but gives slow convergence patterns in constructing the wave functions of systems with interactions that change rapidly with the interparticle distances. The problem is investigated here for the three-nucleon ground state and a number of NN potential models. A faster convergence is obtained by enlarging the hyperspherical harmonic basis in a simple way. Such a behavior should also be important for calculations of the bound state of larger systems and of breakup scattering states.