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Spectrum balancing (SB) techniques optimize transmission and can significantly improve digital subscriber lines (DSL) services. In the literature, the DSL system optimization is typically formulated as a rate maximization problem. However, there is an increasing interest in minimizing the considerable amount of power consumed by telecommunication networks. Few works in the SB literature have explored algorithms for power minimization. It is known that some existing solutions for rate maximization can be converted into power minimization algorithms. This relation has not been fully explored and, consequently, the area lacks results regarding what can be achieved with power minimization SB algorithms. This work aims to diminish this gap. First, the equivalence between rate maximization and power minimization problems is formalized. Second, extended versions of some rate maximization SB algorithms are proposed for power minimization purposes and evaluated through simulations. In addition, the power-usage capabilities and convergence characteristics of each extended SB algorithms is discussed.