Using two detectors to time individual scattered particles, time-of-flight, medium-energy backscattering has established a new standard for depth resolution by ion backscattering and has been suggested as a means to measure very low levels of contamination on semiconductor surfaces. This paper sets forth a criterion for backscattering sensitivity to trace contaminants based upon the limit imposed by sputtering and analyzes the implications of random coincidence background in time-of-flight spectra for reaching this theoretical limit. The effects of high count rates on spectral shape are discussed as are the effects of the quantum efficiencies of start and stop detectors. An integral equation relating an intrinsic spectrum and the corresponding measured data set is presented along with its formal solution.