A process for purifying a lipid composition having predominantly neutral lipid components having at least one long chain polyunsaturated fatty acid is disclosed. The process employs contacting the lipid composition with a polar solvent, such as acetone, wherein the solvent is selected such that contaminants are less soluble in the solvent than is the long chain polyunsaturated fatty acid. The process is typically conducted at cooler temperatures, including about 0° C. Upon precipitation of the contaminants from the lipid composition, a separation is conducted to remove the precipitated material from the lipid composition. The long chain polyunsaturated fatty acids can include ARA, DPA, EPA, and/or DHA. The process of the present invention effectively winterizes lipid compositions, thereby reducing the tendency of such compositions to become hazy.