Crystal-field parameters for dilute Sc-Tb, Sc-Dy, and Sc-Er alloys have been obtained by fitting theoretical expressions to the experimentally measured paramagnetic susceptibility. The initial susceptibility was measured and corrected for the effects of ordering at the lowest temperatures in the hard direction, as investigated by neutron spectroscopy. The crystal-field parameters divided by Stevens factors B20 / α, B40 / β, B60 / γ, and B66 / γ are within the accuracy of their determination independent of the rare-earth solute. A comparison to parameters obtained for dilute Y and Lu rare-earth alloys shows that B40, B60, and B66 are almost independent of the host. B20 / α depends smoothly on the c / a ratio of the host in the decreasing order Y, Lu, Sc.