Novel developments of the so-called controlled evolution of level sets <Ramananjaona et al., 2001b>, which is devoted to shape identification of homogeneous scattering obstacles buried in a known space from time-harmonic wave field data, are considered herein. The emphasis is twofold: regularization of the geometry of the sought shape-enforced via a speed of motion of the level set in (pseudo)time and space resulting from the minimization of a properly penalized objective functional; and improvement of the convergence of the scheme itself by a choice of a time step adapted to the evolution of the level set and to the sought decrease of the objective functional. Key elements of the theoretical analysis are given, and several numerical examples illustrate pros and cons.