Of various published theories of adaptive control of progeny sex ratio only two are plausible, a physiological theory by Trivers & Willard, and a demographic theory by Verner. The first applies to species in which sons and daughters impose different costs on parents, and in which only one or very few young are produced at once. They ought to show positive correlations in the sex of successive offspring and high sex-ratio variance among progenies. Verner's theory postulates a minimization of competition for mates in neighbourhoods subject to random fluctuation in sex ratio. Optimal progenies would exactly match the population's evolutionary equilibrium sex ratio. There would be little variance among progenies. Evidence from vertebrates is unfavourable to either theory and supports, instead, a non-adaptive model, the purely random (Mendelian) determination of sex. The apparent absence of parental control of progeny sex ratio is a serious theoretical difficulty.