Pre-integrated volume rendering has become one of the most efficient and important techniques in three dimensional medical visualization. It can produce high-quality images with less sampling. However, two important issues have received little attention throughout the ongoing discussion of preintegration: Skipping over empty-space and the size of lookup table for a transfer function. In this paper, we present a novel approach for empty-space skipping using the overlapped-min-max block. Additionally, we propose a new approximation technique to reduce the dependent texture size so that it decreases the size of texture memory and the update time. We demonstrate performance gain and decreasing memory consumption for typical renditions of volumetric data sets.