The paper demonstrates two new improvements for the design procedure that increase the computational efficiency of an aerodynamic shape optimization procedure. The numerical procedure is based on discrete sensitivity analysis to compute the design gradient information as opposed to the traditional finite difference approach. To reduce the number of design variables, the first improvement to the method in question is the use of a Bezier-Bernstein polynomial parametrization of the designed surface. This procedure, which has found wide success in the grid generation field, can accurately represent a complex surface shape with a relatively small number of geometric control points. The second improvement involves the replacement of the usual algorithm with a more efficient flow solver based on Newton's method. The efficiency of the new design procedure is demonstrated by optimizing the shape of an internal- external nozzle configuration.