This article is a sequel of [J.-A. De ´side ´ri, Hierarchical optimum-shape algorithms using embedded Be ´zier parameterizations, in: Y. Kuznetsov et al., (Ed.), Numerical Methods for Scientific Computing, Variational Problems and Applications, CIMNE, Barcelona, 2003], in which we defined formally a hierarchical shape optimization method based on a multi-level shape representation by nested Be ´zier parameterizations (FAMOSA), and [J.-A. De ´side ´ri, A. Janka, Multi-level shape parameterization for aerodynamic optimization -application to drag and noise reduction of transonic/supersonic business jet, in: E. Heikkola et al., (Ed.), European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), Jyva ¨skyla, 24-28 July 2004] where we conducted some preliminary numerical experiments of shape optimization in aerodynamics. Here, we are testing the full multi-level optimum-shape algorithm (analogous in logical structure to the classical full multigrid method). Second, we propose a technique for parameterization self-adaptivity. Both methodological enhancements are assessed by novel numerical experiments on an inverse shape model problem, confirming both are very effective.