The invention relates to the manufacture of certain polyunsaturated compounds employing a particular application of the Mitsonobu reaction in the presence of at least one anti-oxidant. We have found a method of making a pharmaceutically-acceptable polyunsaturated ester or thioester compound directly, which can ultimately be converted to the advantageous ketone compounds, in which unwanted oxidation and cis/trans isomerization are substantially reduced or eliminated using particular Mitsonobu chemistry.