Time-driven sensor networks are devoted to the continuous reporting of data to the user. Typically, their topology is that of a data-gathering tree rooted at the sink, whose vertexes correspond to nodes located at sampling locations that have been selected according to user or application requirements. Thus, generally these locations are not close to each other and the resulting node deployment is rather sparse. In a previous paper, we developed a heuristic algorithm based on simulated annealing capable of finding an optimal or suboptimal data-gathering tree in terms of lifetime expectancy. However, despite the enhanced lifetime, the overall link distance is not optimized, fact that increases the need for additional resources (relay nodes). Therefore, in this paper we propose the Link Distance Reduction algorithm, with the goal of reducing link distances as long as network lifetime is preserved. The benefits of this new algorithm are evaluated in detail.