We give a drawing of Kn in three dimensions in which vertices are placed at integer grid points and edges are drawn crossing-free with at most one bend per edge in a volume bounded by O(n2.5 ). Article Type Communicated by Submitted Revised concise paper September 2005 February 2006 A preliminary version of this work was presented at Graph Drawing 2005. Research supported in part by NSERC Canada. inria-00103923,version1-19Nov2007 Author manuscript, published in "Journal of Graph Algorithms and Applications 10, 2 (2006) 287-295"