Previous research has demonstrated that search and memory for items within natural scenes can be disrupted by "scrambling" the images. In the present study, we asked how disrupting the structure of a scene through scrambling might affect the control of eye fixations in either a search task (Experiment 1) or a memory task (Experiment 2). We found that the search decrement in scrambled scenes was associated with poorer guidance of the eyes to the target. Across both tasks, scrambling led to shorter fixations and longer saccades, and more distributed, less selective overt attention, perhaps corresponding to an ambient mode of processing. These results confirm that scene structure has widespread effects on the guidance of eye movements in scenes. Furthermore, the results demonstrate the trade-off between scene structure and visual saliency, with saliency having more of an effect on eye guidance in scrambled scenes.