Classic rangeland theory advocates stocking rangelands at relatively low and constant levels. This theory has been labelled inappropriate for savanna rangelands, because savannas are strongly influenced by stochastic processes. Opportunistic strategies that force animal numbers to track available forage have been proposed as an alternative management paradigm. However, no studies have examined whether these opportunistic strategies are sustainable or optimal. We developed a simulation model of a savanna rangeland to identify optimal, sustainable strategies for the management of extensive rangelands. We optimised the utility of agents who are motivated by economic, production or ecological factors under both deterministic and stochastic conditions. In all cases we found that it was optimal to manage the system conservatively and not opportunistically. Moreover, it was optimal to manage more conservatively under stochastic conditions. Key elements of the conservative strategy were to stock at low levels and to use fire to control tree abundance and thereby maintain the system in a grass dominated state. We conclude that opportunistic strategies of range management although intuitively appealing are not optimal. © 2006 Elsevier B.V. All rights reserved