The biocompatible lattice structures and implants disclosed herein have an increased or optimized lucency, even when constructed from a metallic material. The lattice structures can also provide an increased or optimized lucency in a material that is not generally considered to be radiolucent. Lucency can include disparity, maximum variation in lucency properties across a structure, or dispersion, minimum variation in lucency properties across a structure. The implants and lattice structures disclosed herein may be optimized for disparity or dispersion in any desired direction. A desired direction with respect to lucency can include the anticipated x-ray viewing direction of an implant in the expected implantation orientation.