Optimal escape theory predicts that animals should balance the costs and benefits of flight. One cost of not fleeing is the ongoing cost of monitoring an approaching predator. We used a phylogenetic meta-analysis to test the general hypothesis that animals should initiate flight soon after they detect a predator-the 'flush early and avoid the rush' hypothesis. We found a large, significant overall relationship between the distance at which animals were approached or first detected a threat and the distance at which they fled. While these results are the first general test of the flush early and avoid the rush hypothesis, future work will be required to determine whether animals flush early to reduce ongoing attentional costs, or if they flush early as a form of risk reduction.