Interactive rendering of large surfaces, defined by isosurfaces or otherwise constructed, demands hierarchical data structures which accurately represent a surface at multiple levels of detail. Construction of a hierarchy of models may be integrated with the extraction of isosurfaces or may additionally be performed as a post-process. In our mesh reduction work, arbitrary precision and topological consistency can be attained, while preserving both the geometry of the surface as well as any number of scalar functions defined on the surface. Our algorithm follows the general structure of a point-deletion approach to simplification. The addition of error bounds which are propagated through successive deletions of vertices provides global error control on both the geometry and any number of functions defined.