New differential cross section data for seven target nuclei were analysed using a microscopic model. Particular care was taken to ensure that the absolute magnitude of the cross sections was correctly measured. The predicted direct or one-step (t, 3He) reaction did not account for the magnitude of the data except for forward angles and A⩾40. The calculations were estended to include the contributions from two-step or sequential single-nucleon transfers. Calculations were made using the second-order DWBA and zero-range or full finite-range forms. In the latter the non-orthogonality between the basis states in the two-step transfers was included. The transfer amplitudes were deduced from comparisons of predicted angular distributions with data obtained from the (t, α) and (t, d) reactions, and from amplitudes determined by repeating previously reported shell-model calculations. The full finite-range DWBA calculations which included non-orthogonality terms, accounted for both the shape and magnitude of the data within a factor of 3 in the worst case. The (t, α) reaction angular distributions are, however, poorly predicted.