Non-mechanistic models of competition suggest that harming one of two competing species will increase the population density of the other. These models also suggest that any change in a fitness component of one competitor will make the densities of the two competitors change in opposite directions. However, models of competition that incorporate resource dynamics show that neither conclusion holds generally. Reducing the consumption abilities of one competitor may decrease the population size of the other by decreasing resource overexploitation by the first and thereby increasing its density. It is also possible for decreased consumption abilities of one species to increase the population densities of both species, when the increased density of the focal species is offset by its decreased ability to consume the main resources of its competitor. Finally, decreases in consumption may have the effects predicted by phenomenological models; a decrease in the focal species and an increase in its competitor. Unstable systems may exhibit more complicated patterns of changes in densities with changes in consumption rates. These counterintuitive effects depend on the presence of overexploitation of biotic resources, about which little is known. More generally, there have been few theoretical or empirical studies examining the indirect effects of changes in consumption rates of a focal species in a food web; these are termed ‘trait-initiated indirect effects’. A better understanding of the potential consequences of altered consumption rates will be important for understanding biotic shifts in communities undergoing environmental change, and in using simple community modules to understand larger food webs.