Exome sequencing is being offered for children with undiagnosed conditions to identify a primary (causative) variant. Parental preferences for learning secondary (incidental) variants are largely unexplored. Our objective was to characterize values and beliefs that shape parents' preferences for learning their children's sequencing results. We conducted semi-structured interviews with 25 parents of 13 minor probands with a variety of rare genetic conditions. Parents were asked to discuss their preferences to receive four types of results from exome sequencing. Many parents preferred to receive all types of results. Parents had the most positive attitudes toward learning about variants that predispose to disorders treatable or preventable in childhood. They had reservations about learning about predispositions for untreatable adult-onset conditions and carrier status for recessive conditions. Parents described their success in coping with their child's condition as evidence for an ability to manage any additional negative health information. They felt responsible for learning about secondary variants, desiring a gain in control over their child's health. Our findings suggest that investigators should incorporate parents' perceptions of the value in receiving secondary variant information about their children when designing studies employing exome sequencing.