Generic wraparound aerodynamic shape optimization technology is presented and applied to a modern commercial aircraft wing in transonic cruise. The wing geometry is parameterized by a novel domain-element method, which uses efficient global interpolation functions to deform both the surface geometry and corresponding computational fluid dynamics volume mesh. The technique also provides a method that allows geometries to be parameterized at various levels, ranging from global three-dimensional planform alterations to detailed local surface changes. Combining all levels of parameterization allows for free-form design control with very few design variables. The method provides an efficient combined shape parameterization and high-quality mesh deformation technique that is totally independent of mesh type (structured or unstructured). Optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient-based optimizer by finite differences. The entire optimization suite has also been parallelized to allow optimization with highly flexible parameterization in practical times. Results are presented for highly constrained optimizations of the modern aircraft wing in transonic cruise, using three levels of parameterization (number of design variables) to assess the effect of parameterization level on the optimization. The highest-level optimization results in a totally-shock-free geometry wtih an associated substantial reduction in drag.