We developed a simulation of the detailed model of virulence evolution that indicates that spatial structure constrains disease virulence. The mean-field approximation predicts evolution to criticality; any small increase in virulence capable of dynamical persistence is favored. However, pair approximation of the detailed model agrees with the simulation spatial structure constraining disease virulence. Increased spatial clustering reduces the maximal virulence capable of single-strain persistence and, more importantly, reduces the convergent-stable virulence level under strain competition. The spatially detailed model predicts that increasing the probability of superinfection, for given difference in virulence, increases the likelihood of between-strain coexistence. When strains differing in virulence can coexist ecologically, our results may suggest policies for managing diseases with localized transmission. Comparing equilibrium densities from the pair approximation, we find that introducing a more virulent strain into a host population infected by a less virulent strain can sometimes reduce total host mortality and increase global host density.