Processes for producing biodiesel compositions are disclosed. FFAs present in the triglycerides can be removed by reaction with isobutylene, or by Kolbe electrolysis. The Kolbe electrolysis can be performed on the starting material, or on the crude glycerol. The triglycerides are transesterified to form alkyl esters of the fatty acids and glycerol. The transesterification reaction can be catalyzed by an alkoxide, rather than a hydroxide, to help keep the glycerol by-product dry. The alkoxide salt can be neutralized by reaction with a dry acid, such as gaseous hydrogen chloride or sulfuric acid, and the resulting alcohol removed by distillation, and at least a portion of the neutralized salt can be removed by filtration or decantation. The process can provide improved biodiesel yields, and glycerol pure enough for use directly in glycerol ether manufacture.