Distributions of pairwise differences often called "mismatch distributions" have been extensively used to estimate the demographic parameters of past population expansions. However, these estimations relied on the assumption that all mutations occurring in the ancestry of a pair of genes lead to observable differences (the infinite-sites model). This mutation model may not be very realistic, especially in the case of the control region of mitochondrial DNA, where this methodology has been mostly applied. In this article, we show how to infer past demographic parameters by explicitly taking into account a finite-sites model with heterogeneity of mutation rates. We also propose an alternative way to derive confidence intervals around the estimated parameters, based on a bootstrap approach. By checking the validity of these confidence intervals by simulations, we find that only those associated with the timing of the expansion are approximately correctly estimated, while those around the population sizes are overly large. We also propose a test of the validity of the estimated demographic expansion scenario, whose proper behavior is verified by simulation. We illustrate our method with human mitochondrial DNA, where estimates of expansion times are found to be 10-20% larger when taking into account heterogeneity of mutation rates than under the infinite-sites model.