In this paper, we show that routing algorithms may exploit not only the flexibility obtained by crossing network dimensions in any order but also the one obtained in the same network dimension thanks to the availability of bidirectional channels. We analyze the behavior of both deadlock avoidance and recovery adaptive routing algorithms exploiting this increased routing flexibility, comparing them with previous proposals, in order to evaluate the contribution of the additional routing freedom on network performance. Simulation results show that this simple improvement in the routing algorithm allows to achieve improvements in throughput up to 45% in networks with low radix, for the uniform distribution of message destinations.