Respecting the confidentiality of personal data contributed to genomic studies is an important issue for researchers using genomic sequencing in humans. Although most studies adhere to rules of confidentiality, there are different conceptions of confidentiality and why it is important. The resulting ambiguity obscures what is at stake when making tradeoffs between data protection and other goals in research, such as transparency, reciprocity, and public benefit. Few studies have examined why participants in genomic research care about how their information is used. To explore this topic, we conducted semi-structured phone interviews with 30 participants in two National Institutes of Health research protocols using genomic sequencing. Our results show that research participants value confidentiality as a form of control over information about themselves. To the individuals we interviewed, control was valued as a safeguard against discrimination in a climate of uncertainty about future uses of individual genome data. Attitudes towards data sharing were related to the goals of research and details of participants' personal lives. Expectations of confidentiality, trust in researchers, and a desire to advance science were common reasons for willingness to share identifiable data with investigators. Nearly, all participants were comfortable sharing personal data that had been de-identified. These findings suggest that views about confidentiality and data sharing are highly nuanced and are related to the perceived benefits of joining a research study.