The resonant acceleration and heating of solar wind minor ions via interactions with a spectrum of dispersive or nondispersive undamped ion-cyclotron waves are investigated. The principal goal is to determine how the dimensionless parameters of the problem affect the heating and acceleration processes. In addition, simple physical interpretations of the heating and acceleration are given. The exact numerical evaluations of the heating and acceleration rates imply that (1) the total heating rate is roughly proportional to the mass of the ion; (2) dispersive waves should lead to ni>na>np, where i refers to ions heavier than He++; (3) dispersive waves have a slight tendency to yield ∂Ti/∂t>(mi/ma)∂Ta/∂t, while non-dispersive waves have a slight tendency to yield ∂Ti/∂t<(mi/ma)∂Ta/∂t. The predictions of this model are compared with observations and may offer an explanation for some observed properties of minor ions.