NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user’s interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.