The Gini index is the most commonly used measure of income inequality. Like any single summary measure of a set of data, it cannot capture all aspects that are of interest to researchers. One of its widely reported flaws is that it is supposed to be overly sensitive to changes in the middle of the distribution. By studying the effect of small transfers between households or an additional increment in income going to one member of the population on the value of the index, this claim is re-examined. It turns out that the difference in the rank order of donor and recipient is usually the most important factor determining the change in the Gini index due to the transfer, which implies that transfers from an upper income household to a low income household receive more weight that transfers involving the middle. Transfers between two middle-income households do affect a higher fraction of the population than other transfers but those transfers do not receive an excessive weight relative to other transfers because the difference in the ranks of donor and recipient is smaller than the corresponding difference in other transfers. Thus, progressive transfers between two households in the middle of the distribution changes the Gini index less than a transfer of the same amount from an upper income household to a lower income household. Similarly, the effect on the Gini index when a household in either tail of the distribution receives an additional increment is larger than when a middle-income household receives it. Contrary to much of the literature, these results indicate that the Gini index is not overly sensitive to changes in the middle of the distribution. Indeed, it is more sensitive to changes in the lower and upper parts of the distribution than in the middle.