For a given family of parametric fitting functions, such as polynomials or splines of different order, computed spectroscopic quantities are more consistent, i.e., have smaller uncertainties, when a physics-based guiding function is used as a reference, instead of directly fitting highlevel ab initio data. The best results appear to be obtained when the difference between the highlevel data and the guiding function is a linear function of bond length. The technique may be especially advantageous for noisy data, as from stochastic electronic-structure methods, because a low-order polynomial can more easily fit the data while averaging the noise. The same strategy may be useful for encoding experimental data or for describing dipole moment surfaces. Meaningful spectroscopic predictions can be obtained from as few as two high-level data points. Comparing the results from two guiding potentials provides a systematic and efficient way to select geometries for high-level calculation.