Optimization is an indispensable tool in planning of intensity-modulated radiotherapy therapy (IMRT) planning. Conventional planning objectives are designed to minimize the violation of so-called dose-volume histogram (DVH) thresholds using penalty functions. In this study, we abandon the usual penalty-function framework and propose planning objectives that more explicitly relate to DVH statistics. The proposed planning objectives are based on mean-tail-dose, resulting in optimization problems of linear programming type. We investigate the potential of the proposed planning objectives as tools for optimizing DVH statistics through juxtaposition with the conventional planning objectives on two patient cases. An obstacle when changing from quadratic penalty functions to optimization of mean-tail-dose is that the dimension of the optimization problem is increased by several orders of magnitude. We demonstrate how to adapt a higher-order interior method to make this problem size manageable.