In Layered Manufacturing, the choice of the build direction for the model inuences several design criteria, including the number of layers, the volume and contact-area of the support structures, and the surface nish. These, in turn, impact the throughput and cost of the process. In this paper, ecient geometric algorithms are given to reconcile two or more of these criteria simultaneously, under three formulations of multi-criteria optimization: Finding a build direction which (i) optimizes the criteria sequentially, (ii) optimizes their weighted sum, or (iii) allows the criteria to meet designer-prescribed thresholds. The algorithms that involve \\support volume" or \\contact area" apply only to convex models, while the algorithms that involve \\surface nish" and \\number of layers" apply to any polyhedral model. Some of the latter algorithms have also been implemented and tested on real-world models obtained from industry. The geometric techniques used in the paper include construction and searching of certain arrangements on the unit-sphere, three-dimensional convex hulls, Voronoi diagrams, point location, and hierarchical representations. Additionally, solutions are also provided, for the constrained versions of two geometric problems, namely polyhedron width and largest empty disk on the unit-sphere. 1