Mutualism describes the biological phenomenon where two or more species are reciprocally beneficial, regardless of their ecological intimacy or evolutionary history. Classic theory shows that mutualistic benefit must be relatively weak, or else it overpowers the stabilizing influence of intraspecific competition and leads to unrealistic, unbounded population growth. Interestingly, the conclusion that strong positive interactions lead to runaway population growth is strongly grounded in the behavior of a single model. This model—the Lotka-Volterra competition model with a sign change to generate mutualism rather than competition between species—assumes logistic growth of each species plus a linear interaction term to represent the mutualism. While it is commonly held that the linear interaction term is to blame for the model's unrealistic behavior, we show here that a linear mutualism added to many other models of population growth will not lead to unbounded growth. We find that when density dependence is decelerative, the effect of mutualism is greater than when density dependence is accelerative. Although there is a greater benefit at equilibrium of a mutualist partner, decelerative density dependence tends to destabilize populations whereas accelerative density dependence is always stable. Incidentally, even when we model density dependence in birth and death rates separately, as long as one of the rates shows accelerative density dependence, populations will always be stable. We interpret these findings tentatively, but with promise for the understanding of the population ecology of mutualism by generating several predictions relating growth rates of mutualist populations and the strength of mutualistic interaction.