Equity issues of the dual income tax (DIT) have until recently been left aside in the field of economics. Since a dual income tax needs different modeling from that for a comprehensive one, this paper offers firstly a quantitative framework to measure redistributive effects; it turns out that this involves both direct and indirect effects. This makes us able to show the conditions for the DIT to be inequality-reducing. The effects of horizontal inequity and reranking are also incorporated into the decomposition analysis. Secondly, partial effects of changes in tax parameters are presented; they are channeled through the direct and indirect effects and are not always straightforward. We find the effects of changes of labor income taxation mostly ambiguous on inequality, while changes in capital income taxation are mostly unambiguous. Thirdly, the new approach is applied to Icelandic data. In Iceland, tax redistribution decreased substantially from 1997 to 2007, largely due to the indirect effects.