Brief Summary: This trial is proposes to build on our experience and is designed to maximize early (day 3-14) and late (day 60-71) donor-derived natural killer (NK) cell expansion and function in vivo. The proposed platform will allow us the unique opportunity to compare in vivo function from a transplanted umbilical cord blood (UCB) source (presumed to contain NK progenitors requiring "education" in the recipient).

Detailed Description: This single center study will determine the feasibility and safety of using a myeloablative conditioning regimen followed (on day 0) by transplantation with double T-cell depleted (TCD) umbilical cord blood (UCB) units where the unit with fewer mononuclear cells (MNCs)/kg will be selected for overnight IL-2 activation prior to infusion. Beginning on day +3, post transplant IL-2 will be administered thrice weekly, not on consecutive days, for a total of 6 doses to expand UCB derived progenitor cells. Post transplant immune suppression prophylaxis will not be administered with the intent to lessen toxicity and allow allogeneic NK cells to function longer providing better anti-leukemic therapy. However if either UCB unit has more than 5% T-cells, the patient will not receive either course of IL-2. Beginning on day +60 after transplantation, a second course of IL-2 will be administered thrice weekly, not on consecutive days, for a total of 6 doses with the purpose of enhancing the in vivo expansion and education of NK cells derived from engrafting UCB cells.