Processes for obtaining fatty acids with reduced content of by-products, wherein unrefined fats or oils are subjected to steam stripping in a counter-current column to produce a bottom fraction of de-acidified fats or oils, a first distillate consisting mainly of fatty acids and glycerides, and a second distillate comprising fatty acids and essentially all unwanted ketones, aldehydes and phenols, and the bottom fraction containing the de-acidified fats or oils is combined with the first distillate containing fatty acids and glycerides.