While it now appears likely that sympatric speciation is possible, its generality remains contentious. If it really is rare, then most natural populations must not fit the assumptions of sympatric speciation theory. A better understanding of these assumptions may help identify when sympatric speciation is or is not likely. This paper investigates two such assumptions: that genetic variation for stringent assortative mating is not limiting and that females are not penalized for mating assortatively. Simulations demonstrate that the speed of sympatric speciation is very sensitive to the population's capacity for stringent assortative mating and is potentially extremely slow. The rapid divergence often thought to be a hallmark of sympatric speciation may only occur in a restricted area of parameter space.