This paper develops a framework for locally deforming either a parametric surface or hierarchical subdivision surface to match a set of positional and energy minimizing constraints. The positional constraints can be obtained from a wide variety of existing interfaces, and the framework produces a smooth, local and stable deformation through solving a simple local least-squares. We use an indexing scheme to localize optimization to only contributing control points. These points are found and measured by using basis functions or by tracking subdivision mask operations. We demonstrate our framework on B-spline and Loop subdivision surfaces.