Abstract- Power and energy consumption of communication net-works contribute to the resource demand and hence they impact the sustainability of the society. Transmission links form basic parts ofcommunication networks and thus they add to the overall communica-tio nnetworlks' resourcedemand. Therefore, it is important to optimize transmission links in order to support the energy-efficient design ot communication networks. In transmission systems the constellation size in general is a degnee of freedom when designing or adapting a transmission link. In this article, multilevel baseband transmission via additive white Gaussian noise (AWGN) channels and over copper cables is optimized with respect to minimum power and energy demand, respectively - for the relevant case of given throughput and fixed transmission quality of a transmission link. The results are two-fold: In the AWGN case the minimum power and energy is utilized at the smallest possible constellation size. In case of band- limited base band transmission over twisted-pair copper wires with linear equalization the optimum constellation size increases as the band limitation becomes stronger, ie, as the cable gets longer al fixed bit rate or as the bit rate is increased at fixed link length. The optimization of the constellation size enables significant power and energy savings per link in the range of 25 % to approximately 90 % compared to a conventional two-level baseband system.