The enterprise of virulence management attempts to predict how social practices and other factors affect the evolution of parasite virulence. These predictions are often based on parasite optima or evolutionary equilibria derived from models of host-parasite dynamics. Yet even when such models accurately capture the parasite optima, newly invading parasites will typically not be at their optima. Here we show that parasite invasion of a host population can occur despite highly nonoptimal virulence. Fitness improvements soon after invasion may proceed through many steps with wide changes in virulence, because fitness depends on transmission as well as virulence, and transmission improvements can overwhelm nonoptimal virulence. This process is highly sensitive to mutation supply and the strength of selection. Importantly, the same invasion principle applies to the evolution of established parasites, whenever mutants arise that overcome host immunity/resistance. A host population may consequently experience repeated invasions of new parasite variants and possible large shifts in virulence as it evolves in an arms race with the parasite. An experimental study of phage lysis time and examples of mammalian viruses matching some of these characteristics are reviewed.