A method is disclosed for producing a stable pipelineable blend from a heavy residue of a catalytic hydroconversion process operating at high (60-80%) conversion rate by blending the heavy residue with a virgin bitumen, such as a bitumen produced from the Peace River or Cold Lake oil sand deposits in Alberta, Canada, and/or with a Wabasca virgin heavy crude oil wherein the 524° C.+ Fraction of the blend is controlled such that: 1) The blend comprises less than 40 vol % of heavy 524° C.+ components, i.e. components which boil at atmospheric pressure at a temperature above about 524 Degrees Celsius; and 2) The 524° C.+ fraction in the blend comprises less than about 80 vol % of heavy residue originating from the hydroconversion process.