 This study will begin with a dose of T cells known not to cause GvHD even in haploidentical recipients, even when the T cells administered have not first been allodepleted. Dose escalation will follow a traditional up and down method, but as results become available they will be used to determine subsequent dose levels by the continual reassessment method. Initially, 2 patients will be entered beginning at dose level 1. Each and every patient will receive up to three additional injections of T cells at the same dose, at monthly intervals, provided there is no evidence of grade 2 or higher GVHD, until total T cell numbers are 1000ul. 