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It has been widely recognized that physical layer impairments, including power losses, must be taken into account when routing optical connections in transparent networks. In this paper we study the problem of constructing light-trees under optical layer power budget constraints, with a focus on algorithms which can guarantee a certain level of quality for the signals received by the destination nodes. We define a new constrained light-tree routing problem by introducing a set of constraints on the source-destination paths to account for the power losses at the optical layer. We investigate a number of variants of this problem, we characterize their complexity, and we develop a suite of corresponding routing algorithms; one of the algorithms is appropriate for networks with sparse light splitting and/or limited splitting fanout. We find that, in order to guarantee an adequate signal quality and to scale to large destination sets, light-trees must be as balanced as possible. Numerical results demonstrate that existing algorithms tend to construct highly unbalanced trees, and are thus expected to perform poorly in an optical network setting. Our algorithms, on the other hand, are designed to construct balanced trees which, in addition to having good performance in terms of signal quality, they also ensure a certain degree of fairness among destination nodes. While we only consider power loss in this work, the algorithms we develop could be appropriately modified to account for other physical layer impairments, such as dispersion.