A method of treating a subject in need of a non-syngeneic cell or tissue graft is disclosed. The method comprising: (a) transplanting into a subject a dose of T cell depleted immature hematopoietic cells, wherein the T cell depleted immature hematopoietic cells comprise less than 5 x 105 CD3+ T cells per kilogram body weight of the subject, and wherein the dose comprises at least about 5 x 106 CD34+ cells per kilogram body weight of the subject, and wherein the T cell depleted immature hematopoietic cells are obtained by separating the T cells from the immature hematopoietic 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 kilogram body weight, thereby treating the subject.
