We present cross sections for electron-impact ionization and simultaneous ionization plus excitation of helium by electron impact. The results are obtained from a fully nonperturbative close-coupling formalism using our B-spline R-matrix approach. A large number of pseudostates in the expansion of the wave function represent the coupling to the ionization continuum. We obtain excellent agreement with the directly measured experimental cross section ratios (Bellm et al., Phys. Rev. A 75, 042704 (2007)) for ionization leaving the residual He⁺ ion in either the 1s ground state or the n = 2 (2s + 2p) excited states.