The last 20 years have seen a significant evolution in the literature on horizontal inequity (HI) and have generated two major and "rival" methodological strands, namely, classical HI and reranking. We propose in this paper a class of ethically flexible tools that integrate these two strands. This is achieved using a measure of inequality that merges the well-known Gini coefficient and Atkinson indices, and that allows a decomposition of the total redistributive effect of taxes and transfers in a vertical equity effect and a loss of redistribution due to either classical HI or reranking. An inequality-change approach and a money-metric cost-of-inequality approach are developed. The latter approach makes aggregate classical HI decomposable across groups. As in recent work, equals are identified through a nonparametric estimation of the joint density of gross and net incomes. An illustration using Canadian data from 1981 to 1994 shows a substantial, and increasing, robust erosion of redistribution attributable both to classical HI and to reranking, but does not reveal which of reranking or classical HI is more important since this requires a judgement that is fundamentally normative in nature.