Processes allowing coexistence of trees and grasses in tropical savannas have long intrigued ecologists. Early theories focused on climatic controls, but a conceptual model has emerged suggesting that savanna trees are subject to a fire-mediated recruitment bottleneck, with frequent fires preventing recruitment of saplings into the tree layer and maintaining biomass well below its climate-determined upper bound. We propose that this conceptual model has been overemphasised in northern Australia, where tree abundance is more strongly controlled by water availability. The dominant trees, eucalypts, have a remarkable capacity to grow through the ‘fire trap’ to reach fire-resistant sizes. This fire tolerance makes eucalypts relatively unresponsive to management-imposed reductions in fire frequency and intensity. Other trees in these savannas are typically more fire sensitive and respond positively to such management. There are suggestions that savanna fire management could lead to increases in woody biomass, but we contend that if tree biomass is strongly limited by water availability, then potential increases in tree biomass are relatively limited, at least in relation to the dominant eucalypt component. There is potential to increase the biomass of the more fire-sensitive non-eucalypts, but the upper bound of non-eucalypt tree biomass in these eucalypt-dominated systems remains poorly understood.