Advances in DNA sequencing technology open new possibilities for public health genomics, especially in the form of general population preventive genomic sequencing (PGS). Such screening programs would sit at the intersection of public health and preventive health care, and thereby at once invite and resist the use of clinical ethics and public health ethics frameworks. Despite their differences, these ethics frameworks traditionally share a central concern for individual rights. We examine two putative individual rights—the right not to know, and the child’s right to an open future—frequently invoked in discussions of predictive genetic testing, in order to explore their potential contribution to evaluating this new practice. Ultimately, we conclude that traditional clinical and public health ethics frameworks, and these two rights in particular, should be complemented by a social justice perspective in order adequately to characterize the ethical dimensions of general population PGS programs.