In this paper an attempt is made to elaborate on the behavioral assumptions underlying a simulation model published in a previous volume of this journal (Heer and Smith, 1968). The present paper contains a discussion of the ways in which a fall in the death rate of children will affect the desirability of another birth if the family's objective is to have a son surviving to the father's sixty-fifth birthday. The death rate affects both the expected costs of and benefits from an additional birth. An examination of the effects of a decline in child mortality indicates that the benefits from an additional birth fall and the expected costs rise as a result of the decline. Thus a death rate will eventually be reached where costs exceed benefits, and parents will not desire an additional pregnancy.