It is an implication of the productive efficiency lemma of Diamond and Mirrlees that intermediate goods should not be taxed in a world of constant returns to scale and perfect competition. Three simple models are analysed to examine whether this conclusion can be extended to accommodate imperfect competition. The importance of returns to scale and the form of the production function are emphasised and, where applicable, welfare-improving and optimal tax schemes are described that include taxes on intermediate goods. If all technologies are Leontief, productive efficiency remains desirable.