Abstract: Precise depth calculation is of crucial importance in graphics rendering. Improving precision raises the quality of all downstream graphical techniques that rely on computed depth (e.g., depth buffers, soft and hard shadow maps, screen-space ambient occlusion, and 3D stereo projection). In addition, the domain of correctly renderable scenes is expanded by allowing larger far-to-near plane ratios and smaller depth separation between mesh elements. Depth precision is an ongoing problem because visible artifacts continue to plague applications from interactive games to scientific visualizations despite advances in graphics hardware. par In this article we present and analyze two methods that greatly impact visual quality by automatically improving the precision of depth values calculated in a standard perspective-divide rendering system such as OpenGL or DirectX. The methods are easy to implement and compatible with 1/Z depth-value calculations. The analysis can be applied to any depth projection based on the method of homogeneous coordinates.