The reflection of light ions from heavy random targets has been calculated within the single-collision approximation on the basis of essentially the same physical model as Schiøtt's adaptation of the LSS range theory to light ions. An accurate effectivepower approximation has been utilized to evaluate a number of physical quantities relating to reflected ions under the assumption of Thomas-Fermi scattering. Analytical results as well as universal curves are presented for reflected-energy spectra integrated over ejection angle, particle and energy reflection coefficients, and quantities derived from these. Good agreement with experimental results is obtained for ε≳, where ε is Lindhard's energy parameter. The results are compared with those from previous calculations on the basis of transport theory and computer simulation. An estimate is given of the single-collision tail of the light-ion range profile. Qualitative corrections for beam attenuation and recoil energy loss are presented in appendices.