A method for re-refining used oils comprises contacting feedstock comprising purified used oil with extraction solvent to perform continuous liquid-liquid solvent extraction, to produce an extract stream comprising the extraction solvent and an extract dissolved in the extraction solvent. The feedstock and the extraction solvent are agitated by a variable speed agitator during the solvent extraction at a selected agitation speed. The extract is separated from the extraction solvent and subjected to a continuous flow liquid phase hydrogenation treatment to produce an oil product. A system for performing the method includes a purification unit for purifying the used oil; an extraction column for extracting the extract from the feedstock; and a continuous flow liquid phase hydrogenation unit. The extraction column comprises an agitator configured to agitate the feedstock and the extraction solvent flowing through the extraction column at a variable agitation speed.