Geometrical algorithms have been the main subject of research in the field of real time sound rendering. These algorithms are variants of the image source and ray tracing algorithms, enhanced with improvements that speed up substantially their performance. The fundamental concepts behind the improvements achieved up to now was the reduction of the processed information and the acceleration of the actual processing. In this paper, we show how altering the traversal method affects significantly the algorithm's performance. These optimizations alter its behavior, providing better results for real time purposes. We separate the techniques into three major categories and we propose a stochastic Monte Carlo algorithm which involves optimizations based on prioritization.