This invention relates to a novel method for economically processing vacuum residue from heavy crude oils by selectively processing the difficult and easy components in reactors whose design and operating conditions are optimized for the specific feed. The process utilizes an integrated solvent deasphalting (SDA)/ebullated-bed design wherein the heavy vacuum residue feedstock is initially sent to an SDA unit operated with C.sub.4/C.sub.5 solvent to achieve a high deasphalted oil (DAO) yield. The resulting SDA products, namely asphaltenes and DAO are separately treated in ebullated-bed reactor(s) systems whose design and operating conditions are optimized for a particular feedstock. The resulting net conversion, associated distillate yield and product qualities are greatly improved relative to treatment of the entire residue feedstock in a common ebullated-bed reactor system.