This study suggests that high values of the Gini Index of Inequality may be related to the skewness rather than to the dispersion of income distributions. Since skewness to the right and dispersion should have opposite effects on social welfare, a new index GA is proposed, which adjusts the Gini Index for the asymmetry of income distributions. Illustrations based on data on the distributions of household incomes in various countries in 1968 confirm the relevance of the suggestions made.