Suggested is a process for obtaining fatty acids with reduced content of by-products, characterised in that (a) unrefined fats or oils are subjected to steam stripping in a counter-current column to produce (i) a bottom fraction of de-acidified fats or oils, (ii) a first distillate consisting mainly of fatty acids and glycerides, and (iii) a second distillate comprising fatty acids and essentially all unwanted ketones, aldehydes and phenols; and (b) said bottom fraction (i) containing the de-acidified fats or oils and said first distillate (ii) containing fatty acids and glycerides are combined.