Developmental theories of false belief understanding traditionally focus on either cognitive control - the executive function children need to reason flexibly and select appropriate responses or cognitive content - the information children need to reason about mental states. However, tasks that measure false belief typically involve both control and the processing of content, requiring the conflicting dimensions of belief and reality to be identified and separated out for success. In adult models, performance in the task is driven by the detection and resolution of response-conflict, an ability that appears to develop postnatally. In developmental models, the picture is less clear. With a group of children aged 3 years 9 months, we show that training that invokes response-conflict but has no related false belief content improves performance in false belief tasks, while similar training that both invokes response-conflict and provides appropriately structured domain relevant knowledge improves performance still further. Neither of these interventions affect the performance of children just 8 months younger, suggesting that the development of the ability to detect and resolve response-conflict may be an essential ingredient to the acquisition of false belief understanding.