This invention relates to a novel integrated method for economically processing vacuum residue from heavy crude oils. This is accomplished by utilizing a solvent deasphalter (SDA) in the first step of the process with a C3/C4/C5 solvent such that the DAO product can thereafter be processed in a classic fixed-bed hydrotreater or hydrocracker. The SDA feed also includes recycled stripper bottoms containing unconverted residue/asphaltenes from a downstream steam stripper unit. The asphaltenes from the SDA are sent to an ebullated-bed reactor for conversion of the residue and asphaltenes. Residue conversion in the range of 60-80% is achieved and asphaltene conversion is in the range of 50-70%. The overall residue conversion, with the DAO product considered non-residue, is in the range of 80 W %-90 W % and significantly higher than could be achieved without utilizing the present invention.