Conversion of vegetable-derived triglycerides to fatty acid methyl esters (FAMEs) is a popular approach to the generation of biodiesel fuels and the basis of a growing industry. Drawbacks of the strategy are that (a) the glycerol backbone of the triglyceride is discarded as waste in this synthesis, and (2) many natural triglycerides are multiply-unsaturated or fully saturated, giving inferior performance and causing engine problems with long-term use. Here, we show that catalysis by iridium complex 1 can address both of these problems through selective reduction of triglycerides high in polyunsaturated fatty esters to FAMEs with high oleate concentration. This is realized using hydrogen imbedded in the triglyceride backbone, concurrently generating lactate as a value-added C3 product. Additional methanol or glycerol as a hydrogen source enables reduction of corn and soybean oils to >80% oleate.