The population growth rates implied by parental attempts to be highly certain of having a surviving son for old-age support are investigated. At life expectancies of 40 to 65 years, family-planning “strategies” using contraception are found to imply markedly lower growth rates (1.01.5 percent vs. 2.5 percent) than are both commonly observed and also previously derived by Heer and Smith. In contrast to strategies relying only on sterilization, contraceptive spacing of births permits parents to buy time and information. In particular, they can postpone deciding whether to have another child until they see if their infant son will survive the earliest years of childhood. These results suggest that many less developed countries might achieve a substantial reduction in birth rates, provided that family-planning programs emphasized contraception as well as sterilization and effectively communicated the idea of spacing births. Factors bearing on the range of applicability of the old-age-security hypothesis, and any results and policies derived from it, are also briefly analyzed.