The role of the ICT sector in our daily life is causing a significant growth of the power consumed by the network equipment. In this context, transparent WDM networks represent a promising solution for reducing the power consumption of telecom networks. For this reason transparent WDM networks attract a lot of interest and several power-aware routing and wavelength assignment algorithms are available in the literature. These approaches, however, seem to consider power minimization as the only parameter to be optimized. Little or no attention is given to other important network aspects, e.g., connection requests blocking. Such approaches may not always be advisable, especially in core WDM networks where high performance levels must be considered in the first place. This article aims at providing a different insight to the PA-routing problem. It follows the intuition that in some cases relaxing the power minimization constraint can have beneficial effects on the overall network performance, especially on the blocking probability. A novel approach, referred to as Weighted Power-Aware Lightpath Routing (WPA-LR), is proposed and evaluated using two continental core networks. Our results confirm the presence of a trade-off between power savings and blocking probability.