We will use flow cytometric and MRD technologies, to determine the presence of persistent disease , and will include in this study only patients with a limited amount of residual disease (<1% leukemic lymphoblasts among normal bone marrow cells). We will use the same MRD methods to monitor the effects of treatment infusions. We do not expect that the conditioning regimen will have much effect by itself on leukemic cell counts, as the patients eligible for the study will have disease that is resistant to many anti-leukemic drugs. Nevertheless, because the conditioning regimen itself may have some salutary effects, it will be important to screen the peripheral blood and/or bone marrow for the presence of leukemic blast cells through all stages of the procedure, i.e., before, during, and after conditioning and after the NK cell infusion. The presence of leukemic cells in will be closely monitored by flow cytometry or PCR amplification of antigen-receptor genes (sensitivity for either method: 1 leukemic cell in 10,000) to shed some light on the relative effect of each intervention.