We present a framework for accurate and robust extraction of parametric models of different types. It includes a mechanism that lets each model type determine its domain of applicability. The framework is general in the sense that it can be described and implemented without specifying the following components: a domain of application, a particular type of data, a set of admissible model types, and a specific fitting technique. It is a conceptually clean approach to model extraction, and its implementation provides a highly reusable algorithm which can be easily linked with a specific set of admissible types of models and with a specific fitting function. The framework consists of four components: exploration, selection, fit, and a final selection. The exploration is a dynamic data-driven masking technique that proposes a set of models from which the selection chooses the ones that explain the data with minimal description length. Selection is performed by tabu search, a discrete optimization technique that outperforms annealing techniques on many classical optimization problems. Our robust fitting technique, which increases the accuracy of the selected models, may change the classification of data elements which requires the final selection. We apply our framework to simultaneously extract straight lines and ellipses from 2D data, and planes and spheres from 3D data.