Measurements with Solar and Heliospheric Observatory (SOHO)/Charge, Element, and Isotope Analysis System (CELIAS) in high-speed solar wind show that some minor ions such as O6+ have a relatively high drift velocity; however, other ions such as Fe9+ tend to lag behind oxygen by a few tens of km/s <Hefti et al., 1998>. This subtle observational feature has not yet been understood. A possible way, based on the quasi-linear theory of cyclotron resonance, of understanding this phenomenon is presented in this paper. The charge per mass of the ion O6+ and Fe9+ are different, a fact which results in different features of the ion-cyclotron resonance with waves. In plasma with protons, drifting alpha particles, and electrons, the dispersion relation of cyclotron waves has two branches. The oxygen ions tend to resonate with the inward propagating waves of the left-hand-polarized (LHP) first branch and the outward propagating waves of the LHP second branch. These resonances may together lead to a velocity distribution with a central velocity higher than the proton (solar wind) bulk velocity by about 50 km/s at 1 AU. The Fe9+ ions tend to resonate with both the inward and outward propagating waves of the first branch and may thus form a velocity distribution with a central velocity very near the proton bulk velocity. These analytical results are shown to be supported by numerical results from a two-dimensional simulation based on the quasi-linear diffusion equation. The limitations of the present analysis and further work, which should be done to support the ideas proposed here, are also discussed.