We present a new dual-level approach to representing potential energy surfaces in which a very small number of high-level electronic structure calculations are combined with a lower-level global surface, e.g., one defined implicitly by neglect-of-diatomic-differential-overlap calculations with specific reaction parameters, to generate the potential at any geometry where it may be needed. We interpolate the potential energy surface with a small number of accurate data points (the higher level) that are placed along the reaction path by using information on the global shape of the potential from less accurate calculations (the lower level). We confirm the findings of Ischtwan and Collins on the usefulness of single-level schemes including Hessians, and we delineate the regime of usefulness of single-level schemes based on gradients or even single-point energies. Furthermore we find that dual-level interpolation can offer cost savings over single-level schemes, and dual-level methods employing Hessians, gradients, or even only simple energy evaluations can yield reasonable potential energy surfaces with relatively low cost, with the potentials being more accurate along the reaction path. For all methods considered in this paper the accuracy of the interpolation for our test cases is lower when the potentials at points significantly removed from the reaction path are predicted from data that lie entirely on the reaction path.