Efficient and deadlock-free routing is critical to the performance of networks-on-chip. In this paper we present an approach that can be coupled to any adaptive routing algorithm to improve the performance with a minimal overhead on area and energy consumption. The proposed approach introduces the concept of Neighbors-on-Path to exploit the situations of indecision occurring when the routing function returns several admissible output channels. A selection strategy is developed with the aim to choose the channel that will allow the packet to be routed to its destination along a path that is as free as possible of congested nodes. Performance evaluation is carried out by using a flit-accurate simulator on traffic scenarios generated by both synthetic and real applications. Results obtained show how the proposed selection policy applied to the Odd-Even routing algorithm outperforms other deterministic and adaptive routing algorithms both in average delay and energy consumption.