We present a method for improving the accuracy and efficiency of interpolation methods, in which an analytical zeroth-order potential-energy surface is employed as a reference surface. To investigate and test the method, we apply it to hydrogen peroxide where there exists an accurate analytical surface which we take as the "exact" surface for obtaining the energies and derivatives for fitting and assessing the accuracy. Examples are given for four-dimensional and six-dimensional surfaces interpolated by using either the modified Shepard or second-degree interpolating moving least-squares approach, with comparisons for cases with and without using the zeroth-order potential. (C) 2004 American Institute of Physics.