Results from the artificial life community show that under some conditions evolving populations converge on broader, but less fit peaks in the fitness landscape and avoid more fit, but narrower peaks. Results from the evolutionary computation community show that over time genotypes evolve to become more resilient, where resiliency (or genetic robustness) is defined as the ability of an individual to resist the potentially negative effects of genetic operations. This article demonstrates a previously unobserved evolutionary dynamic: in populations initially favoring a low, broad fitness peak, increases in resiliency result in the population shifting to a higher, narrower fitness peak. In these cases increasing resiliency is a necessary precondition for finding narrower peaks.