This article concerns some problems associated with the progressive taxation of personal incomes. The main focus of the paper is the development of progressive tax scale meeting the principle of justice. The taxes are considered fair, if all the taxpayers have been withdrawn the same proportion of utility from their earnings. The utility of money spent for consumption, which is characterized by marginal utility decrease, is meant. This utility is presented in the article by the logarithmic function, which arguments are the ratios of incomes of the citizens to the subsistence level. The particular way of building smooth tax functions satisfying the above formulated rule of fair taxation is proposed. It is proved, that the implementation of such functions requires just progressive taxation. And, after that, a procedure of forming multi-layered scales approximating these smooth tax functions is also presented. A few concrete examples of fair progressive scales are shown. A curious fact is marked that the scale of the progressive income tax adopted in France with good accuracy corresponds to the proposed methodology. In the final part of the article some rules for application of such scales taking into account citizen’s marital status are shortly discussed, as well as some other questions relating to the possible transition from the currently used in Russia flat scale to a progressive scale of taxation of personal incomes.