OUTLINE: This is a multicenter, controlled, randomized trial. Patients are assigned to high or low risk groups and randomized to the control or treatment arms. Patients are stratified by risk group and by site. Mobilization, apheresis, and successful cryopreservation of the minimum number of CD34 cells for transplant has to be achieved prior to initiating cytoreductive therapy. Following intensive cytoreductive therapy, patients receive either unselected peripheral blood stem cells (PBSC) together with the control graft versus host disease (GVHD) prophylaxis regimen or CD34+ cells isolated from PBSC with cyclosporine. In the control group, GVHD prophylaxis consists of two drug therapies, cyclosporine and methotrexate. The cyclosporine is administered first by IV continuous infusion and then later orally, twice a day, in decreasing increments for 180 days. Methotrexate is administered by IV on days 1, 3, 6, and 11. Cyclosporine is discontinued after day +180 if there is no evidence of GVHD. In the treatment group, GVHD prophylaxis consists of T cell depletion of the transplant product using the Isolex positive selection procedure (Isolex selected CD34+ cells) and cyclosporine. The cyclosporine is administered at the same doses and increments as in the control group. In cases where there still is acute or chronic GVHD, the patient is given the appropriate salvage regimens. Patients are followed monthly for 6 months after transplant, and then for 2 years to monitor relapses.