The ionization cross-sections of H and He+ from the ground state and excited 2s state for incident electron energies from threshold to about four times threshold energy are calculated. The strong coupling between the hydrogenic Is, 2s and 2p states is explicitly allowed for in the initial state, and the final state is taken to be an appropriate combination of Coulomb wave functions of the two outgoing electrons. Comparison with experiment for ground-state ionization shows that the method is an unprovement over the Born approximation particularly for He+. New results are presented for the Born approximation in He+ ionization and for the Born-Oppenheimer approximation for both H and He+ ionization. Finally, conclusions are drawn from the results concerning the validity of methods for calculating ionization cross-sections from excited states.