This is a prospective multicenter, open-label, randomized trial in which individuals with liver failure due to hepatitis C or to nonimmune nonviral causes undergo liver transplantation and receive immunosuppression with a calcineurin inhibitor and corticosteroids. Corticosteroids are tapered in the 3 months after transplantation and the calcineurin inhibitor is continued. Participants are regularly assessed for evidence of allograft rejection. One year after transplantation, participants eligible for withdrawal are randomly assigned in a 4 to 1 ratio to immunosuppression withdrawal or to maintenance. Participants assigned to withdrawal undergo a scheduled taper over approximately 1 year.