When an initial income distribution pattern Y = (Y"1, Y"2,...Y"n) is given, the operation of a balanced budget fiscal program that involves taxation and transfer payments leads to a disposable income pattern D = (D"1, D"2,...D"n). Let I(X) be an index of income inequality. When the total budget (i.e. total taxes collected) is fixed, the problem is to design a "most equitable" fiscal program that minimizes I(D). It will be shown that the solution can be readily calculated from Y and is independent of I(X) as long as the Dalton's "principle of transfer" is satisfied. This condition is met by a family of indices of inequality including the Gini coefficient, Theil index, coefficient of variation and the Atkinson index.