This paper presents a new approach for generating coarse-level approximations of topologically complex models. Dramatic topology reduction is achieved by converting a 3D model to and from a volumetric representation. Our approach produces valid, error-bounded models and supports the creation of approximations that do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Several simple to implement versions of our approach are presented and discussed. We show that these methods perform significantly better than other surface-based approaches when simplifying topologically-rich models such as scene parts and complex mechanical assemblies.