Data from the inelastic scattering of 40-MeV protons by Ni58 and Ni60 are presented and analyzed in terms of a coupled-channel approach. Previous discrepancies between the experimental and theoretical distributions of the first excited 2+ states are removed. The nature of coupled-channel calculations at this energy is discussed, with reference to absorptive strengths and form factors. 4+ states around 2.5-MeV excitation are shown to require one-phonon mixing in order to explain the observed cross sections. Spin-parity assignments are given for states at 3.2-, 5.1-, and 6.1-MeV excitation in Ni60.