It is a challenge to predict the response of a large, complex system to a perturbation. Recent attempts to predict the behavior of food webs have revealed that the more complex the system, the more precisely the elements of the system must be measured. As a result, the amount of effort needed to understand a system grows quickly with its complexity. Here, we show that not all elements must be measured equally well, suggesting a more efficient allocation of effort to understanding complex systems is possible. We then develop an iterative technique to efficiently arrive at this solution. Finally, in our assessment of model food webs, we find that it is most important to precisely measure the mortality and predation rates of large, generalist, top predators. Prioritizing the study of such species will make it easier to understand the response of complex food webs to perturbations.