Patients were randomly assigned to receive either a T-cell depleted or a non-depleted transplant. Two methods of T-cell depletion were in use: an anti-CD3 monoclonal antibody, T10B9, plus complement, or counterflow elutriation plus the Ceprate column. Each method of T-depletion was part of a package that included a specific pre-transplant conditioning regimen and additional GvHD prophylaxis. Patients randomized to the non-T-cell depleted arm received a conditioning regimen containing cyclophosphamide and total body irradiation, and a GvHD prophylaxis regimen of cyclosporin and methotrexate. A total of 410 patients were enrolled. Enrollment ended October 31, 2000.