Abstract. We present a simple and efficient distributed method for determining the transmission power assignment that maximises the lifetime of a data-gathering wireless sensor network with stationary nodes and static power assignments. Our algorithm determines the transmission power level inducing the maximum-lifetime spanning subgraph of a network by means of a distributed breadth-first search for minmax-power communication paths, i.e. paths that connect a given reference node to each of the other nodes so that the maximum transmission power required on any link of the path is minimised. The performance of the resulting Maximum Lifetime Spanner (MLS) protocol is validated in a number of simulated networking scenarios. In particular, we study the performance of the protocol in terms of the number of required control messages, and compare it to the performance of a recently proposed Distributed Min-Max Tree (DMMT) algorithm. For all network scenarios we consider, MLS outperforms DMMT ...