Populations exposed to a high mutation rate harbor abundant deleterious genetic variation, leading to depressed mean fitness. This reduction in mean fitness presents an opportunity for selection to restore fitness through the evolution of mutational robustness. In extreme cases, selection for mutational robustness can lead to flat genotypes (with low fitness but high robustness) outcompeting fit genotypes (with high fitness but low robustness)—a phenomenon known as survival of the flattest. While this effect was previously explored using the digital evolution system Avida, a complete analysis of the local fitness landscapes of fit and flat genotypes has been lacking, leading to uncertainty about the genetic basis of the survival-of-the-flattest effect. Here, we repeated the survival-of-the-flattest study and analyzed the mutational neighborhoods of fit and flat genotypes. We found that the flat genotypes, compared to the fit genotypes, had a reduced likelihood of deleterious mutations as well as an increased likelihood of neutral and, surprisingly, of lethal mutations. This trend holds for mutants one to four substitutions away from the wild-type sequence. We also found that flat genotypes have, on average, no epistasis between mutations, while fit genotypes have, on average, positive epistasis. Our results demonstrate that the genetic causes of mutational robustness on complex fitness landscapes are multifaceted. While the traditional idea of the survival of the flattest emphasized the evolution of increased neutrality, others have argued for increased mutational sensitivity in response to strong mutational loads. Our results show that both increased neutrality and increased lethality can lead to the evolution of mutational robustness. Furthermore, strong negative epistasis is not required for mutational sensitivity to lead to mutational robustness. Overall, these results suggest that mutational robustness is achieved by minimizing heritable deleterious variation.