Genetic incompatibilities can emerge as a by-product of genetic divergence. According to Dobzhansky and Muller, alleles at different loci that have fixed in different genetic backgrounds may be incompatible when brought together in a hybrid. Orr showed that the number of Dobzhansky–Muller incompatibilities (DMIs) should accumulate faster than linearly—i.e., snowball—as two lineages diverge. Several studies have attempted to test the snowball model using data from natural populations. One limitation of these studies is that they have focused on predictions of the snowball model but not on its underlying assumptions. Here we use a computational model of RNA folding to test both predictions and assumptions of the snowball model. In this model, two populations are allowed to evolve in allopatry on a holey fitness landscape. We find that the number of DMIs involving pairs of loci (i.e., simple DMIs) does not snowball—rather, it increases approximately linearly with divergence. We show that the probability of emergence of a simple DMI is approximately constant, as assumed by the snowball model. However, simple DMIs can disappear after they have arisen, contrary to the assumptions of the snowball model. This occurs because simple DMIs become complex (i.e., involve alleles at three or more loci) as a result of later substitutions. We introduce a modified snowball model—the melting snowball model—where simple DMIs can become complex after they appear. The melting snowball model can account for the results of the RNA folding model. We also find that complex DMIs are common and, unlike simple ones, do snowball. Reproductive isolation, however, does not snowball because DMIs do not act independently of each other. We conclude that the RNA folding model supports the central prediction of the snowball model that the number of DMIs snowballs, but challenges some of its underlying assumptions.