"The rich are getting richer" implies that the population income distributions are getting more right-skewed and heavy-tailed. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are all mean-based. In view of this, Professor Gastwirth sounded an alarm back in 2014 by suggesting to incorporate the median into the definition of the Gini index, although noted a few shortcomings of his proposed index. In the present paper we make a further step in the modification of classical indices and, to acknowledge the possibility of differing viewpoints, arrive at three median-based indices of inequality. They avoid the shortcomings of the previous indices and can be used even when populations are ultra-heavy tailed, that is, when their first moments are infinite. The new indices are illustrated both analytically and numerically using parametric families of income distributions, and further illustrated using a real data set of capital incomes of fifteen countries. We also discuss the performance of the indices from the perspective of the Pigou-Dalton principle of transfers.