We present a new method for detail-preserving 3D shape editing that decouples the complexity of the modeling algorithm from the geometric complexity of the object being edited. A deformation graph, which can be constructed automatically or designed by hand, parameterizes the allowable shape deformations as a collection of affine transformations acting on local regions of the model. Shape editing is formulated as a nonlinear optimization problem where detail preservation is encoded directly by specifying that the affine transformations should be rotations. Editing constraints are formulated on the surface itself, which hides the underlying deformation model and allows the user to select and position arbitrary vertices. Our reduced deformable model can handle complex non-manifold surfaces with multiple connected components, allowing efficient direct manipulation of large, highly detailed meshes, unprocessed raw scanner output, and even point clouds with no connectivity information.