Deacidified fats and/or oils are made by the process which comprises the steps of: (a) reacting a technical triglyceride having an acid value of up to about 60 and a stoichiometric excess of a lower alcohol having from 1 to 4 carbon atoms and from about 0.5% to about 5% by weight of a lipase to form a pre-esterification product having an acid value of from about 0.5 to about 10, (b) optionally removing water and unreacted alcohol from the pre-esterification product, (c) further reacting the pre-esterification product from step (a) or (b) with additional lower alcohol to form a post-esterification reaction product having an acid value of from about 0.1 to about 0.5.