A series of computer-simulation models relating mortality level to fertility behavior and to rates of natural increase assuming that couples made use of a perfect means of birth control, that they wanted to be highly certain of having at least one son survive to the father’s 65th birthday, and that all women were biologically capable of having the same number of children were reported earlier. A model identical to one presented earlier but assuming women to be of variable fecundity is presented here; the results are quite similar. Also, the results of models assuming that parents want to be highly certain of at least two surviving children regardless of sex are compared with models assuming parental desire to be highly certain of at least one surviving son. At high levels of mortality the rates of natural increase are quite similar. When mortality is at intermediate to medium-low levels, the two-surviving-children model shows a lower rate of natural increase than the surviving-son model. At very low levels of mortality, such as now experienced by the most advanced nations, the two-surviving-children model manifests a higher rate of natural increase than the surviving-son model.