International trade in nonnative species generates economic benefits but also introduces many harmful invasive species. Recent advances in nonnative species screening tools enable useful predictions of invasiveness which can be combined with estimates of impacts to effectively manage the trade-off between the benefits and costs of this trade. Despite this, most countries maintain an essentially “open door” policy where almost all nonnative species are allowed for introduction until they prove problematic. This approach implicitly favors minimizing one particular type of assessment error—mistakenly excluding safe species, or “false positives.” However, a comprehensive approach to management of species trade should involve balancing the trade-off between false positives and “false negatives” (mistakenly accepting invasive species). Barriers to implementing risk assessment tools include the perception that because assessment tools are imperfect they are not suitable for decision-making. However, recent economic research shows that, relative to an open door approach, “shutting the screen door” with imperfect but informative screening tools, to allow flow of only those species of acceptable invasion risk, increases the net benefits of trade. Given that these tools are relatively straightforward to apply, we argue that policy-makers should no longer allow the perfect to be the enemy of the good.