In this article, we propose new approaches for solving the useful-skew tree (UST) routing problem [Xi and Dai 1997]: clock routing subject to general skew constraints. The clock layout synthesis engine of our UST algorithms is based on the deferred-merge embedding (DME) paradigm for the zero-skew tree (ZST) [Edahiro 1992; Chao et al. 1992] and bounded-skew tree (BST) [Cong and Koh 1995; Huang et al. 1995; Kahng and Tsao 1997; Cong et al. 1998] routings; hence, the names UST/DME and Greedy-UST/DME for our UST algorithms. Our novel contribution is that we simultaneously perform skew scheduling and tree routing so that each local skew range is incrementally refined to a skew value that minimizes the wirelength increase during the bottom-up merging phase of DME. As a result, not only is the skew schedule feasible, but also the wirelength increase is minimized at each merging step of clock tree construction. The experimental results show very encouraging improvement over the previous BST/DME algorithm on three ISCAS89 benchmarks under general skew constraints in terms of total routing wirelength.