Mismatch distributions are histograms showing the pattern of nucleotid
e (or restriction) site differences between pairs of individuals in a
sample. They can be used to test hypotheses about the history of popul
ation size and subdivision (if selective neutrality is assumed) or abo
ut selection (if a constant population size is assumed). Previous work
has assumed that mutations never strike the same site twice, an assum
ption that is called the model of infinite sites. Fortunately, the res
ults are surprisingly robust even when this assumption is violated. We
show here that (1) confidence regions inferred using the infinite-sit
es model differ little from those inferred using a model of finite sit
es with uniform site-specific mutation rates, and (2) even when site-s
pecific mutation rates follow a gamma distribution, confidence regions
are little changed until the gamma shape parameter falls well below i
ts plausible range, to roughly 0.01. In addition, we evaluate and reje
ct the proposition that mismatch waves are produced by pooling data fr
om several subdivisions of a structured population.