We report a numerical study of the effect of interface alloying and band-alignment on the Auger recombination processes of core/shell nanocrystals. Numerical calculations are carried out using a two-band Kane Hamiltonian. Smooth interfaces are found to suppress Auger recombination, the strength of the suppression being very sensitive to the core size. The use of type-II structures constitutes an additional source of suppression, especially when the shell confines electrons rather than holes. We show that "magic" sizes leading to negligible Auger recombination [Cragg and Efros, Nano Letters 10 (2010) 313] should be easier to realize experimentally in nanocrystals with extended interface alloying and wide band gap. ; Comment: 12 pages (preprint format), 6 figures