Recent work on incidental findings, concentrating on the difficult problems posed by the ambiguous results often generated by high-tech medicine, has proceeded largely independently from recent work on medical researchers' ancillary-care obligations, the obligations that researchers have to deal with diseases or conditions besides the one(s) under study. This paper contends that the two topics are morally linked, and specifically that a sound understanding of ancillary-care obligations will center them on incidental findings. The paper sets out and defends an understanding of ancillary-care obligations, which is based on the idea that when participants signed up for a study they may -- independently of their beliefs and expectations and of those of the researchers -- be taken to have partially entrusted certain aspects of their health into the researchers' hands. This partial entrustment model of ancillary-care obligations, in turn, has substantive implications for how to deal ethically with incidental findings; for instance, it suggests that researchers have no moral obligation to hunt for incidental findings.