Abstract: The invention is an energy-efficient improvement in a continuous deasphalting process in which a mixture of viscous hydrocarbon oils with resins and/or asphaltenes is contacted with a quantity of pure or mixed hydrocarbon solvents including, but not limited to, propane, butane, pentane, hexane, heptane, isomers thereof, and unsaturated hydrocarbons of similar molecular weights, in order to separate a primary extract phase comprising high viscosity oil, resins and/or asphaltenes, and solvent. The primary raffinate phase is further contacted with an additional quantity of solvent comprising similar components to those in the primary solvent (but not necessarily identical thereto) to separate a secondary extract phase comprising high viscosity oil and solvent, and a secondary raffinate phase comprising resins and/or asphaltenes and solvent. The contacting step may be repeated as often as desired to make additional extract phases which are recovered separately.