In this paper we describe methods to efficiently visualize multiple intersecting volumetric objects. We introduce the concept of V-Objects. V-Objects repbstract properties of an object connected to a volumetric data source. We present a method to perform direct volume rendering of a scene comprised of an arbitrary number of possibly intersecting V-Objects. The idea of our approach is to distinguish between regions of intersection, which need costly multi-volume processing, and regions containing only one V-Object, which can be processed using a highly efficient brick-wise volume traversal scheme. Using this method, we achieve significant performance gains for multi-volume rendering. We show possible medical applications, such as surgical planning, diagnosis, and education.