The evolutionary advantages of genomic imprinting are puzzling. We propose that genomic imprinting evolved as a mechanism that maximizes the interindividual variability in the rates of gene expression for dosage-sensitive loci that, with minimal unrelated deleterious effects, can alter the phenotype over a wide continuum. We hypothesize (1) that genomic imprinting provides a previously suggested haploid selective advantage (HSA); (2) that many imprinted genes have evolved mechanisms that facilitate quantitative hypervariability (QH) of gene expression; (3) that the combination of HSA and QH makes possible a rapid and reversible form of imprinting-dependent evolution (IDE) that can mediate changes in phenotype; and (4) that this enhanced adaptability to a changing environment provides selective advantage to the population, as an assisted form of evolution. These mechanisms may have provided at least one of the driving forces for the evolution of genomic imprinting in mammals. The rheostat model suggests that both genetic and epigenetic variants can contribute to an integrated mechanism of mixed Mendelian and non-Mendelian inheritance and suggests the possibility that the majority of variants are not intrinsically deleterious but, depending on the environment, are each potentially advantageous. Moreover, this would be a reversible form of evolution, with the ability not only to protect a silent allele from selection for many generations but to reactivate and expand it in the population quickly.