Genomic research can reveal ‘unsolicited’ or ‘incidental’ findings that are of potential health or reproductive significance to participants. It is widely thought that researchers have a moral obligation, grounded in the duty of easy rescue, to return certain kinds of unsolicited findings to research participants. It is less widely thought that researchers have a moral obligation to actively look for health-related findings. This paper examines whether there is a moral obligation, grounded in the duty of easy rescue, to actively hunt for genomic secondary findings. We begin by showing how the duty to disclose individual research findings can be grounded in the duty of easy rescue. Next, we describe a parallel moral duty, also grounded in the duty of easy rescue, to actively hunt for such information. We then consider six possible objections to our argument, each of which we find unsuccessful. Some of these objections provide reason to limit the scope of the duty to look for secondary findings, but none provide reason to reject this duty outright. We argue that under a certain range of circumstances, researchers are morally required to hunt for these kinds of secondary findings. Although these circumstances may not currently obtain, genomic researchers will likely acquire an obligation to hunt for secondary findings as the field of genomics continues to evolve.