This paper presents a new packet-forwarding mechanism for underwater acoustic sensor networks. The solution, termed MPR for Multi-Point Relay, makes use of both periodic control messages and information piggybacked in data packets to find the best relay towards the final destination. Relay nodes are selected according to (recent) historical information considering different metrics, i.e., link quality, link liveliness and symmetry. MPR uses the collected information to route packets around connectivity voids and shadow zones. The performance of MPR has been compared with that of a flooding-based solution, named EFlood for enhanced flooding. Metrics of interest include packet delivery ratio, endto-end packet latency and introduced overhead. A thorough performance evaluation has been conducted through at-sea experiments, channel replaying and ns2-based simulations. Our results show that MPR offers a stable and reliable solution which is able to scale to scenarios where a large number of nodes or high traffic loads are considered. Moreover, it makes possible to reduce the overhead introduced in the network, reducing the number of transmitted bits up to four times with respect to EFlood.