In recent years, the study of mitochondrial DNA (mtDNA) variation has entered a new phase with an increasing emphasis on interpretations of demographic, rather than phylogenetic, history. Human mtDNA variation fits a "sudden expansion" model, where the human species expanded rapidly in size during the Late Pleistocene. This paper examines the sudden expansion model with the goal of partitioning total mtDNA diversity in contemporary populations into two components--diversity that existed prior to the population expansion and diversity that arose after the expansion. A method is developed for estimating these components. Analysis of mtDNA diversity within selected human populations shows that 64-80% of mtDNA diversity in contemporary populations arose after the expansion, a consequence of a high mutation rate relative to the number of generations since expansion. The basic model is extended to two components of excess diversity in sub-Saharan Africa--differences in population size before the expansion and differences in the timing of expansion. Results suggest that excess sub-Saharan African mtDNA diversity is due to the combined effects of the sub-Saharan African population being larger in size prior to the expansion and expanding earlier.