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Many traditional techniques for "looking inside" volumetric data involve removing portions of the data, for example using various cutting tools, to reveal the interior. This allows the user to see hidden parts of the data, but has the disadvantage of removing potentially important surrounding contextual information. We explore an alternate strategy for browsing that uses deformations, where the user can cut into and open up, spread apart, or peel away parts of the volume in real time, making the interior visible while still retaining surrounding context. We consider various deformation strategies and present a number of interaction techniques based on different metaphors. Our designs pay special attention to the semantic layers that might compose a volume (e.g. the skin, muscle, bone in a scan of a human). Users can apply deformations to only selected layers, or apply a given deformation to a different degree to each layer, making browsing more flexible and facilitating the visualization of relationships between layers. Our interaction techniques are controlled with direct, "in place" manipulation, using pop-up menus and 3D widgets, to avoid the divided attention and awkwardness that would come with panels of traditional widgets. Initial user feedback indicates that our techniques are valuable, especially for showing portions of the data spatially situated in context with surrounding data.