Multiple studies have examined ‘what’ people think about fuel management (perceptions); fewer have examined ‘how’ people think about it (structure of thoughts). In an Australian study, we used Integrative Complexity Theory (ICT) to explore the relationship between how complexly people thought about, and how acceptable they found, three fuel management strategies: prescribed burning, mechanical thinning and livestock grazing. Integrative complexity (IC) was associated with the direction of acceptability of the most familiar practice - prescribed burning, but trust in organizations was associated with acceptability of all strategies. IC was associated with the extremity of acceptability, with higher IC associated with more moderate attitudes. Our findings support the argument that targeting communication to (i) match current IC and (ii) encourage growth in complexity of thinking has potential to encourage more moderate and stable attitudes about fuel management.