Phase-controlled beam-scanning arrays are structures useful for many applications. Adopting the approach introduced in [1], the scanning process is here treated as a special kind of pattern reconfiguration, where all the patterns radiated by the array have the same shape, but are shifted one from each other by a given angular step, so as to realize a discrete beam-scanning. An iterative algorithm is presented for the power synthesis of beam-scanning arrays of arbitrary geometry, based on the alternating projections method. The algorithm allows to reduce the electric field produced by the array in a given near-field region in order to avoid possible interferences and compatibility problems due to the environment surrounding the antenna. In order to ensure the phase-only control, the excitation amplitude of each array element is required to be constant during the scanning process, and only the excitation phases are modified. Furthermore, the amplitudes are not assigned, but are optimized, and the dynamic range ratio (DRR) of such amplitudes can be reduced below a given threshold. This allows to use a simpler and cheaper feeding network.