The effect of the number of parents and their level of inbreeding on the mean and the variance of synthetic varieties was studied for diploids and autotetraploids. The number of parents and their level of inbreeding act in opposing ways. Maximum mean requires a high number of parents and no inbreeding. Maximum variance requires a small number of highly inbred and unrelated parents. When the number of parents increases (k ≥ 2) the coefficients of the components of variance decrease, and the decrease is more rapid for variances associated with increasing order of interactions between genes. The coefficients of components of variance increase as the level of inbreeding of the parents increases and the increase is greater for components associated with increasing order of interactions between genes.Consequently, according to the values of inbreeding depression and the components of genetic variance and heritability, an optimum genetic base may exist, i.e., an ideal combination of the number of parents and the level of their inbreeding. With no inbreeding, selection among synthetics uses mainly additive variance. By increasing the level of inbreeding of the parents, the effects of dominance and of additive X additive variances on genetic advance when selecting among synthetics increase. One cycle of selection among synthetics appears more efficient than individual selection within populations. The problem of population improvement before selecting among synthetics is discussed.