Present invention relates to a process for reducing the MOSH and/or MOAH content from vegetable oil selected from the group consisting of palm-based oil, cocoa butter-based oil and any mixtures thereof, and comprising steps of: a) subjecting the vegetable oil to a short-path evaporation, wherein the short-path evaporation is performed at a pressure of below 1 mbar, at an evaporation temperature in a range of from 235 and 290° C., and with a feed rate per unit area of evaporator surface of the shorth-path evaporation equipment in a range of from 35 to 102 kg/h·m2, and thus obtaining a retentate vegetable oil and a distillate, b) Contacting the retentate vegetable oil with an adsorbent, and c) Subjecting the bleached retentate vegetable oil to a further refining step.