Genetic variability is the clay of evolution, providing the base material on which adaptation and speciation depend. It is often assumed that most interspecific differences in variability are due primarily to population size effects, with bottlenecked populations carrying less variability than those of stable size. However, we show that population bottlenecks are unlikely to be the only factor, even in classic case studies such as the northern elephant seal and the cheetah, where genetic polymorphism is virtually absent. Instead, we suggest that the low levels of variability observed in endangered populations are more likely to result from a combination of publication biases, which tend to inflate the level of variability which is considered 'normal', and inbreeding effects, which may hasten loss of variability due to drift. To account for species with large population sizes but low variability we advance three hypotheses. First, it is known that certain metapopulation structures can result in effective population sizes far below the census size. Second, there is increasing evidence that heterozygous sites mutate more frequently than equivalent homozygous sites, plausibly because mismatch repair between homologous chromosomes during meiosis provides extra opportunities to mutate. Such a mechanism would undermine the simple relationship between heterozygosity and effective population size. Third, the fact that related species that differ greatly in variability implies that large amounts of variability can be gained or lost rapidly. We argue that such cases are best explained by rapid loss through a genome-wide selective sweep, and suggest a mechanism by which this could come about, based on forced changes to a control gene inducing coevolution in the genes it controls. Our model, based on meiotic drive in mammals, but easily extended to other systems, would tend to facilitate population isolation by generating molecular incompatabilities. Circumstances can even be envisioned in which the process could provide intrinsic impetus to speciation.