This paper deals with simplification algorithms for generating coarse-level approximations of both geometrically and topologically complex models. Our main contribution is a new framework called DPS which models a family of topology-reducing simplification algorithms which have in common the use of an intermediate discrete representation of the scene. DPS provides a robust scheme for aggressive simplification of objects and assemblies while guaranteeing valid, error-bounded solid representations. DPS also enables approximations that do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Several instances of DPS algorithms are presented and discussed. We show that DPS methods perform significantly better than other surface-based approaches when simplifying topologically-rich models such as scene parts and complex mechanical assemblies.