Gini coefficients, which measure gross inequalities rather than their unfair components, are often used as proxy measures of absolute or relative distributive injustice in Western societies. This presupposes that the fair inequalities in these societies are small and stable enough to be ignored. This article presents a model for a series of ideal, perfectly just societies, where comfortable lives are equally available to everyone, and calculates the Gini coefficients for each. According to this model, inequalities produced by age and other demographic factors, together with reasonable choices under equal opportunity, can raise the Gini coefficients for perfectly just societies to levels at least as high as those of any current Western country, and can as easily account for differences in Gini coefficients between such societies or within one such society over time. If Gini coefficients at these levels are possible for ideal societies without distributive injustice, then they should not be used as proxy measures of distributive injustice in real societies.