In this paper, we present a general methodology for the improvement of the criteria of a given routing scheme. We study particularly the correlation between deadlock-avoidance and paths' stretch factor [28]. We prove that the methodology preserves deadlock-avoidance. As the methodology starts from a primary communication scheme, we choose routing by Eulerian cycle rules [27] as the primary scheme. To validate the methodology, we apply the resulting routing scheme to the torus network. Then, making a judicious choice with regard to certain parameters, we prove that the result is an adaptive, deadlock-free, minimal and storage efficient routing algorithm for such networks.