We use basic results from graph theory to design two algorithms for constructing 3-dimesional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. Our first algorithm gives drawings bounded by an O(\sqrt(n)) \times O(\sqrt(n)) \times O(\sqrt(n)) box; each edge route containing at most 7 bends. The best previous result generated edge routes containing up to 16 bends per route. Our second algorithm gives drawings having at most 3 bends per edge route. The drawings lie in an O(n) \times O(n) \times O(n) bounding box. Together , the two algorithms initiate the study of bends/bounding box trade-off issues for 3-dimensional grid drawings.