This study addresses three questions : why do inequalities matter for Brazil's development? Why does Brazil occupy a position of very high inequality in the international community? And, What should public policy do about it? Excessive income inequality is unfair, and undesirable on ethical grounds, and can bring adverse effects on economic growth, health outcomes, social cohesion, and crime. Brazil's excessive income inequality is associated to regressive public transfers, less equitable distribution of education, and higher wage differentials. It is thus suggested that Brazil's strategy to fight inequality should focus on four areas that are good for reducing inequality, good for reducing poverty, and good for increasing efficiency, competitiveness, and growth: raising the level, and reducing the inequities of educational attainment, reducing the wage skill premium of post-secondary education, reallocating public expenditure away from excessive, and regressive transfers, and taking advantage of the opportunity to implement an indirect tax reform, that can reduce the inequity of indirect taxation. Despite the absence of explicit tradeoffs between equity, and efficiency, these policies do not benefit everyone, and they do involve inevitable political choices.