Adaptive beam re-shooting is proposed as a solution to overcome essential limitations of the Gaussian Beam Shooting technique. The proposed algorithm is based on iterative frame decompositions of beam fields in situations where usual paraxial formulas fail to give accurate enough results, such as interactions with finite obstacle edges. Collimated beam fields are successively re-expanded on narrow and wide window frames, allowing for re-shooting and further propagation of collimated beams. Closed form formulas used in the course of these re-expansions are presented, as well as first numerical tests of accuracy.