We propose a new representation for multiresolution models which uses volume elements enclosed between the different resolution levels to encode the detail information. Keeping these displacement volumes locally constant during a deformation of the base surface leads to a natural behaviour of the detail features. The corresponding reconstruction operator can be implemented efficiently by a hierarchical iterative relaxation scheme, providing close to interactive response times for moderately complex models. Based on this representation we implement a multiresolution editing tool for irregular polygon meshes that allows the designer to freely edit the base surface of a multiresolution model without having to care about self-intersections in the respective detailed surface. We demonstrate the effectiveness and robustness of the reconstruction by several examples with real-world data.