We present a variational framework for rapid shape prototyping. The modeled shape is represented as a Catmull-Clark multiresolution subdivision surface which is interactively deformed by direct user input. Free-form design goals are formulated as constraints on the shape and the modeling problem is cast into a constrained optimization one. The focus of this paper is on handling multiresolution constraints of different kinds and on preserving surface details throughout the deformation process. Our approach eliminates the need for an explicit decomposition of the input model into frequency bands and the overhead associated with saving and restoring high frequency detail after global shape fairing. Instead, we define a deformation vector field over the model and we optimize its energy. Surface details are considered as part of the rest shape and are preserved during free-form model editing. We explore approximating the solution of the optimization problem to various degrees to balance trade-offs between interactivity and accuracy of the results.