Understanding a volume dataset through a 2D display is a complex task because it usually contains multi-layered inner structures that inevitably cause undesirable overlaps when projected onto the display. This requires us to identify feature subvolumes embedded in the given volume and then visualize them on the display so that we can clarify their relative positions. This article therefore introduces a new feature-driven approach to previewing volumes that respects both the 3D nested structures of the feature subvolumes and their 2D arrangement in the projection by minimizing their occlusions. The associated process begins with tracking the topological transitions of isosurfaces with respect to the scalar field, in order to decompose the given volume dataset into feature components called interval volumes while extracting their nested structures. The volume dataset is then projected from the optimal viewpoint that archives the best balanced visibility of the decomposed components. The position of the optimal viewpoint is updated each time when we peel off an outer component with our interface by calculating the sum of the viewpoint optimality values for the remaining components. Several previewing examples are demonstrated to illustrate that the present approach can offer an effective means of traversing volumetric inner structures both in an interactive and automatic fashion with the interface. 1998 ACM Subject Classification I.3.8 [Computer Graphics]: Application