Quasi-linear velocity-space diffusion coefficients due to L-mode electromagnetic ion cyclotron (EMIC) waves are considered in a multispecies plasma. It is shown, with slight approximations to exact cold plasma theory, that within EMIC pass bands the index of refraction is a monotonically increasing function of frequency. Analytical criteria are then derived which identify ranges of latitude, wavenormal angle, and resonance number consistent with resonance in a prescribed wave population. This leads to computational techniques which allow very efficient calculation of the diffusion coefficients, along the lines previously developed for whistler and ion cyclotron waves in an electron-proton plasma. The techniques are applied to radiation belt electrons at L = 4, for EMIC waves in the hydrogen, helium, and oxygen bands representative of different phases of a magnetic storm. Finally, diffusion coefficients for recovery-phase helium-band EMIC waves are combined with those for typical whistler hiss, resulting in electron precipitation lifetimes substantially less than those due to hiss alone.