Optical ages for 14 sediment samples collected from the post-Howiesons Poort, late Middle Stone Age (MSA) and final MSA deposits at Sibudu, KwaZulu-Natal, South Africa were reported in a companion paper (Jacobs, Z., Wintle, A.G., Duller, G.A.T., Roberts, R.G., Wadley, L. New ages for the post-Howiesons Poort, late and final Middle Stone Age at Sibudu, South Africa. Journal of Archaeological Science, 2008). These ages were based on equivalent dose (D-e) distributions that were overdispersed. In this paper, we investigate factors both internal and external to the grains that may contribute to such higher than expected overdispersion in single grain D-e values. Intrinsic factors accounted for some, but not all, of the observed scatter, and application of a set of rejection criteria filtered grains for which erroneous D-e values would otherwise be calculated. We investigated sediment mixing and differences in the beta dose received by individual grains in their burial environment as two likely reasons for the observed overdispersion. The scatter in D-e distributions for all the samples is best explained by grains that were deposited at the same time and which were well bleached, but that subsequently received a range of beta doses. A procedure is presented for adjusting the measured beta dose rate, and its associated error. We show that using a combination of single grain OSL measurements of D-e, the finite mixture model and adjustment of the beta dose rate, result in stratigraphically consistent ages. These ages are more consistent than the ages obtained from multiple grain aliquot D-e values and the average dose rates for each sample; the multiple grain ages are about 10% older, partly because of the variable dose rate and partly because these aliquots contained grains with undesirable OSL characteristics. (c) 2007 Elsevier Ltd. All rights reserved.