A mismatch distribution is a tabulation of the number of pairwise differences among all DNA sequences in a sample. In a population that has been stationary for a long time these distributions from nonrecombinant DNA sequences become ragged and erratic, whereas a population that has been growing generates mismatch distributions that are smooth and have a peak. The position of the peak reflects the time of the population growth. The signature of an ancient population expansion is apparent even in the low-resolution mtDNA typings described by Merriwether et al. (1991). The smoothness of the mismatch distribution, an indicator of population expansion, is hardly affected by population structure, whereas mean sequence divergence increases in a pooled sample from highly isolated subpopulations.