Determining maximum transmit power by a local node. A method includes identifying one-hop neighbor nodes of the local node in the mesh network. One or more threshold maximum changes in interference caused by the local node increasing its transmit power for each of the one-hop neighbor nodes of the local node are identified. A plurality of power change values are identified. Each power change value in the plurality of power change values corresponds to a power change at the local node that would cause one of the threshold maximum changes in interference to occur at a corresponding one-hop neighbor node of the local node. A lowest power change value from among the plurality of power change values is identified. As a result, power transmitted by the local node is increased, while limiting an increase in power transmitted by the local node to no more than the lowest power change value.