I. To determine whether the rate of leukemia relapse can be decreased for patients with chronic myelogenous leukemia in blast crisis (CML-BC) and Philadelphia chromosome positive acute lymphoblastic leukemia (Ph+ ALL) responsive to imatinib mesylate (or either dasatinib or nilotinib for patients who have imatinib-resistant disease or who are intolerant of imatinib) followed by nonmyeloablative hematopoietic stem cell transplantation (HSCT) compared to historical controls given high-dose conventional allogeneic HSCT or chemotherapy.