Frame based decomposition of fields provides a rigorous, flexible and effective tool to represent planar source field distributions as summations of Gaussian windows. The field radiated by each window can be approximated as a Gaussian beam in its paraxial region. In this context, beam shooting and bouncing techniques have been proposed as an alternative to corresponding ray methods for describing wave propagation in complex environments. Complex-Source beams, which are closely related to Gaussian beams, provide rigorous solutions for several canonical problems. The objective of this paper is to investigate relations between Gaussian beams radiated by frame windows and Complex-Source beams. Such an approach would open the door to extending the applicability of frame decomposition methods, enhancing Gaussian beam shooting by means of solutions provided by Complex-Source beams.