This report is part of a series of numerical studies in optimum-shape design in aerodynamics in which the equations of Fluid Mechanics (typically the Euler Equations for Compressible Perfect Gas) are solved by a Finite-Volum- e-type method over a structured or unstructured mesh, and the aerodynamic shape (wing or airfoil) is optimized w.r.t. some aerodynamic criterion (e.g. lift maximization or drag reduction). We are considering here the two-dimensionnal case in which the shape is an airfoil represented by a Bézier curve whose degree is much smaller than the number of meshpoints on the body surface and we assume that the control points have a priori fixed abscissas and that their ordinates constitute the set of parameters of the optimization. We evaluate by numerical experiments the incidence of this a priori choice on the efficacy of the optimization.