Methods for quantitative conversion of soapstock, lecithin gums, deodorizer distillate and other by-products of vegetable oil refining containing interrupted double bond systems, to products with conjugated double bonds, using a reduced amount of alkali. Less than one mole of alkali per mole of acyl group present is required, thereby greatly reducing the need for added caustic compared with methods using oils, fatty acids and esters as starting materials. The preferred starting materials are soapstocks derived from vegetable oils rich in linoleic acid.