OUTLINE: This is a randomized, double blind, multicenter study. Patients are stratified by age (under 60 vs 60 and over) and center. Allogeneic peripheral blood stem cells (PBSC) are harvested and selected for CD34+ cells on days 5-8. Nonmyeloablative conditioning: Patients receive fludarabine IV over 30 minutes and cytarabine IV over 4 hours (beginning 4 hours after the start of fludarabine infusion) on days -6 to -3 and idarubicin IV over 1-5 minutes on days -6 to -4. Filgrastim (G-CSF) is administered subcutaneously daily beginning on day -2 and continues until blood counts recover. Graft versus host disease prevention: Beginning on day -2, patients receive tacrolimus IV continuously until oral dosing is tolerated. Patients receive tacrolimus in combination with methotrexate on days 1, 3, and 6 after completion of transplantation. Beginning 12 weeks after completion of transplantation, oral tacrolimus is tapered and stopped over 4 weeks. Transplantation: Allogeneic PBSC are infused on day 0. At 4 months posttransplantation, patients with residual Ph+ cells by cytogenetics or FISH OR hematologic or clinical evidence of chronic myeloid leukemia AND without symptomatic chronic graft versus host disease requiring immunosuppressive therapy are randomized to 1 of 2 treatment arms: Arm I: Lymphocytes harvested from the original PBSC donor are processed with the CD8 high density microparticle device to remove all or most CD8+ cells. Patients receive CD8+ cell depleted donor lymphocyte infusion (DLI) IV over 15-30 minutes on the same day of collection. Arm II: Lymphocytes are harvested from the original PBSC donor. Patients receive undepleted DLI IV over 15-30 minutes on the same day of collection. Patients are followed at days 30, 60, 100, and 180, and then periodically through year 5.