Data‐hungry, complex ecosystem models are often used to predict the consequences of threatened species management, including perverse outcomes. Unfortunately, this approach is impractical in the many systems that have insufficient data to parameterize ecosystem interactions or reliably calibrate or validate such models. We devised a different approach composed of a minimum realistic model that guides decisions in data‐ and resource‐scarce systems. We applied our approach to a case study in an invaded ecosystem from Christmas Island, Australia, where there are concerns that cat (Felis catus) eradication to protect native species, including the red‐tailed tropicbird (Phaethon rubricauda), could release mesopredation by invasive rats (Rattus rattus). We used biophysical constraints (metabolic demand) and observable parameters (e.g., prey preferences) to identify the combined cat and rat abundances that could threaten the tropicbird population. The population of tropicbirds was not sustained when predated by 1607 rats (95% credible interval [CI]: 103–5910) in the absence of cats and 21 cats (95% CI: 2–82) in the absence of rats. For every cat removed from the island, the bird's net population growth rate improved, provided rats did not increase by more than 77 individuals (95% CI: 30–174). Thus, in this context, 1 cat is equivalent to 30–174 rats. Our methods are especially useful for on‐the‐ground predator control in the absence of knowledge of predator–predator interactions to determine whether current abundance of predators threatened the prey population of interest; managing only 1 predator species was sufficient to protect the prey species given potential release of another predator; and control of multiple predator species was needed to meet the conservation goal. With our approach limited information can be used for maximum value in data‐poor systems because it shifts the focus from predicting future trajectories to identifying conditions that impede conservation.