This study aims to identify the values of patients to inform policies and infrastructure for biobanking and precision medicine in the face of trade-offs between values. We surveyed breast cancer patients about conditions for receiving research results, partnerships between nonprofit health systems and for-profit companies, and the distribution of financial value generated from research. Survey questions presented trade-offs between values such as maintaining privacy versus receiving research results. Patients generally are willing to be re-identified to receive information about the use of their donated tissue---especially research results. They support public-private partnerships if they accelerate development of new therapies and tend to favor the idea of sharing in financial benefits generated from research on their tissue.