A method of recovering bitumen from a froth utilizes solvent and a single settling vessel having a plurality of internals. The froth is diluted with enough solvent to reduce viscosity and is added to the vessel above the internals. Additional solvent is added below the internals, intermediate the internals or both and is flowed counter-current to the diluted froth flowing downwardly over the internals, forming a gradient of solvent concentration relative to hydrocarbon concentration throughout the internals, acting as multiple stages of separation. The bitumen and other light components, rise with the solvent to the top of the vessel. The heavier components, such as water, solids and asphaltene aggregates fall to the bottom by gravity. Where paraffinic solvents are used, the solvent-to-bitumen ratio (S:B) for the initial dilution of froth is below that at which asphaltenes are rejected. Substantially all asphaltene rejection occurs in the vessel as S:B increases therein.