This paper introduces a new Lorenz dominance criterion that allows ranking income distributions according to centrist measures à la Seidl and Pfingsten (1997). In doing so, it defines α -Lorenz curves by adapting the generalized Lorenz curves to this case. In addition, it provides an empirical illustration of these tools using Australian income data for the period 2001–2008. The results suggest that despite the reduction of relative inequality, inequality increased for most centrist value judgments.