Evolution at high mutation rates is minimally affected by six processes: mutation–selection balance, error catastrophes, Muller’s Ratchet, robustness and compensatory evolution, and clonal interference. Including all of these processes in a tractable, analytical model is difficult, but they can be captured in simulations that utilize realistic genotype-phenotype-fitness maps, as done here by modeling RNA folding. Subjecting finite, asexual populations to a range of mutation rates revealed simple criteria that predict when particular evolutionary processes are important. Populations were initiated with a genotype encoding the most fit phenotype. When purifying selection was strong relative to mutation, the initial genotype was replaced by one more mutationally robust, and the maximally fit phenotype was maintained in a mutation–selection balance where the deleterious mutation rate determined mean fitness. With weaker purifying selection, the most fit genotypes were lost. Although loss of the best genotype was ongoing and might have led to a progressive fitness decline, continual compensatory evolution led to an approximate fitness equilibration. Per total genomic mutation rate, mean fitness was similar for strong and weak purifying selection. These results represent a first step at separating interactions between evolutionary processes at high mutation rate, but additional theory is needed to interpret some outcomes.