An iterative procedure for the synthesis of uniform amplitude focused beam arrays is presented. Specifically, the goal is to optimize the locations of a fixed number of array elements with known excitations in order to synthesize narrow-beam low-sidelobe patterns. Any fixed elements excitations can be handled, although uniform amplitude and equiphase excitations are aimed because of their practical interest. Moreover, the method can be applied to both linear and planar arrays, and there is no restriction regarding the element patterns. On top of being easy to implement, the proposed procedure leads to solutions that either equal or outperform the ones found by previous approaches in various cases of interest.