A method of treating a subject in need of a non-syngeneic cell or tissue graft is disclosed. The methods comprising: (a) transplanting into a subject a dose of T cell depleted immature hematopoetic cells, wherein the T cell depleted immature hematopoetic cells comprise less than 5×105 CD3+ T cells per kilogram body weight of the subject, and wherein the dose comprises at least about 5×106 CD34+ cells per kilogram body weight of the subject, and wherein the T cell depleted immature hematopoetic cells are obtained by separating the T cells from from the immature hematopoetic cells by magnetic cell sorting, and (b) administering to the subject a therapeutically effective amount of cyclophosphamide, wherein the therapeutically effective amount comprises 25-200 mg per body weight, thereby treating the subject.
