Peripheral blood stem cells (PBSC) are collected between days 8 and 12 post induction chemotherapy. Within 4 weeks of PBSC collection, patients receive carmustine IV over 2 hours on day -6, etoposide IV over 2 hours on days -5 to -2, cytarabine IV over 5 minutes twice daily on days -5 to -2, and melphalan IV over 10-15 minutes on day -1. (Alternatively, high dose cyclophosphamide and total body irradiation beginning 2-4 weeks after cyclophosphamide or standard induction chemotherapy priming is also allowed.) PBSC are reinfused on day 0.