SINGLE IONIZATION BY COMPTON SCATTERING ON He and H-. S.Itza-Ortiz(*), J.Wang(+), J.H. McGuire(*), J. Burgdorfer(**) and A. Godunov(*). (*) Tulane University, New Orleans, LA, 70118, U.S.A. (+) University of Massachusetts-Dartmouth, N. Dartmouth, MA, 02747,U.S.A. (**) University of Tennessee, Knoxville, TN, 37996, U.S.A. We calculated the differential cross sections per unit energy tranfer of single ionization by Compton scattering of He and H-. We compare these with the corresponding Compton cross sections by one and two free electrons. We also calculated the total Compton cross sections for He and, for the first time, for H-. We compared them with the total Compton cross sections of one and two free electrons.