Abstract: This paper discusses how to squeeze volume rendering into as few bits per operation as possible while still retaining excellent image quality. For each of the typical volume rendering pipeline stages in texture map volume rendering, ray casting and splatting we provide a quantitative analysis of the theoretical and practical limits for the required bit precision for computation and storage. Applying this analysis to any volume rendering implementation can balance the internal precisions based on the desired final output precision and can result in significant speedups and reduced memory footprint.