In a previous paper1 evidence was presented that patients with chronic leukemias treated by a comprehensive program termed titrated, regularly spaced total body irradiation were able to spend over 80% of their leukemic life spans at their normal occupations and recreations. The number of patients involved, the period of observation, and the methods of analysis used did not permit a statement at that time that life was prolonged by this method of treatment. In the present paper a much larger series of patients is reported over a longer period of time, and the data have been analyzed by Tivey,2 using a modification of the "maximum likelihood method" of Fisher,3 Boag,4 and Lea.5 Evidence is presented in this paper that survival time is significantly prolonged by this program of therapy. METHOD OF THERAPY The method of therapy was described in a previous paper1 and is