Elastic scattering of 12C, 14N, and 16O ions by sulfur has been investigated near the non-Rutherford energy threshold below 31 MeV. Angular distributions in the range 72°-170°have been measured. Decreasing elastic scattering cross sections with increasing angle above a threshold energy and smooth oscillations were observed. As a function of energy, the cross sections fall off rapidly above the threshold energy, rendering heavy-ion backscattering spectrometry practically useless. A classical semiempirical model is introduced for predicting the angular and target dependence of the high-energy limit for 12C, 14N, and 16O ion Rutherford backscattering spectrometry. The present energy thresholds are reproduced by the model within experimental accuracy. © 1995 American Institute of Physics.