In this paper, we present a new clock routing algorithm which minimizes total wirelength under any given path-length skew bound. The algorithm constructs a bounded-skew tree (BST) in two steps: (i) a bottom-up phase to construct a binary tree of shortest-distance feasible regions which represent the loci of possible placements of clock entry points, and (ii) a top-down phase to determine the exact locations of clock entry points. Experimental results show that our clock routing algorithm, named BST/DME, can produce a set of routing solutions with skew and wirelength trade-off.