Preliminary data from other centers has suggested that adoptive immunotherapy with cells from a relative is an effective approach that may improve remission rates and survival in AML and MDS, because they exert anti-cancer effects of their own (so called graft vs leukemia effects) and possibly because they hasten recovery of cell counts from chemotherapy. The Investigators are interested in confirming these data, but also in testing umbilical cord blood cells for the same purpose. Preliminary data indicate that umbilical cord blood cells may have more powerful graft vs leukemia effects and cause fewer side-effects.