We discuss a new minimum density objective for spanning and Steiner tree constructions. This formulation is motivated by the need for balanced usage of routing resources to achieve minimum-area VLSI layouts. We present efficient heuristics for constructing low-density spanning trees, and prove that their outputs are on average within small constants of optimal with respect to both tree weight and density. The minimum density objective can be transparently combined with a number of previous interconnection objectives (e.g., minimizing radius or skew), without affecting the solution quality with respect to these previous metrics. Extensive simulation results suggest that applications to VLSI global routing are promising. 1 Introduction We address a new minimum density objective for spanning and Steiner tree constructions in the Manhattan plane. Our work is motivated by the area minimization requirement inherent in the global routing phase of VLSI layout (the global routing phase entail..