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In this paper optimal discrete dynamic loading algorithms for multicarrier systems employing DMT (discrete multitone) are proposed. The solutions are derived under the additional constraints on either the maximum allowed energy for each subchannel or the maximum size of the QAM constellations that are used. Both dynamic margin maximization and dynamic rate maximization are considered. The optimal solutions to these problems are provided under very general conditions and include as special cases previously known results. The solutions are developed in the framework of matroid theory, resorting to some results concerning the optimality of a greedy algorithm in combinatorial optimization.