The handicap mechanism of sexual selection by female choice has been strongly criticized because it does not cause sexual selection to reinforce viability selection and it cannot account for the origin of mating preferences. However, several models indicate that the handicap mechanism can have important effects when operating in conjunction with Fisher's mechanism in polygynous populations. These models have been criticized because they require that fitness remains heritable indefinitely. I develop a simple haploid model of the handicap mechanism based on nonheritable variation in paternal investment, thus eliminating the problem of heritable fitness. This model produces the same evolutonary dynamics as both simple and quantitative genetic models of the handicap mechanism based on heritable fitness. If the parameters are such that Fisherian runaway selection does not occur in the null model (i.e., the polymorphic equilibria, which lie along the "Fisher line," are stable), then the handicap mechanism turns the Fisher line into an evolutionary trajectory upon which all other trajectories converge. This occurs because Fisher's mechanism generates no net selection on female preference when the population is on the Fisher line, so that any additional source of selection (direct or indirect) on female choice causes the population to evolve deterministically along the Fisher line. This change in the evolutionary dynamics has the important consequence of eliminating the potential for rapid population divergence for mating systems via genetic drift along the Fisher line.