Methods of coherent pumping through dipole-allowed 5d levels of RE ion are proposed for laser cooling. The coherent and complete population transfer between the ground and the first excited levels of 4f multiplet is achieved by using the different Raman techniques, namely two-photon scattering, adiabatic passage method, and π-pulse pumping. It is shown that the multiplication of the number of electrons that participate in cooling cycle leads to increasing of the cooling power and to acceleration of the cooling process. The increasing of cooling efficiency of 0.5% compared to the direct pumping between 4f levels is attained through the use of dipole-allowed optical transitions. Performed estimates show that the sample temperature can achieve 94 K for current purity materials. The calculations are obtained for Yb3+:CaF2 system.