We examine the causes of the asymmetric distributions of dose observed from measurements of the optically stimulated luminescence emitted by small aliquots of fluvial quartz, and deduce that the asymmetry arises as a result of samples being composed of a mix of mainly well bleached grains with grains that were effectively unbleached at the time of deposition. We demonstrate that the shapes of the dose distributions can be used to assess the likelihood that aliquots consist only of grains that were well-bleached at the time of deposition. The more asymmetric the distribution, the greater the probability that the aliquots with the lowest dose most closely represent the true burial dose. Single grains with differing doses are present in each of the samples examined, and the population with the lowest dose gives an optical age consistent with the expected burial age. This result implies that the beta-dose heterogeneity in these deposits is small, and that the effects of micro-dosimetric variations on optical dating of individual grains are not significant for these samples. We demonstrate that single-grain dating of fluvial material is possible and practicable using standard Riso optical dating equipment, and we conclude that application of a new regenerative-dose protocol to single grains of quartz, using the lowest dose population to estimate the burial dose, is the best available means of obtaining reliable luminescence ages for heterogeneously bleached fluvial sediments.