The aim of this paper is to provide a generalization of the Pfähler (1990) and Lambert (1989, 2001) decomposition, which allows us to overcome some limitations of the original methodology. In particular, our proposal avoids the problem of sequentiality when the tax has several types of deductions or allowances, schedules or tax credits. In addition, our alternative decomposition is adapted to the dual income class of tax structures. Moreover, in order to adapt this methodology to real-world taxes, our approach includes the re-ranking effects of real taxes, caused by the existence of differentiated treatments based on non-income attributes. This theoretical proposal is illustrated with an empirical analysis for the Spanish Personal Income Tax reform enforced in 2007.