The hypothesis that futures prices are unbiased predictors of spot prices is a joint hypothesis that markets are efficient and risk premia are absent. Rejection of unbiasedness could be caused by the failure of either premise. Here cointegration techniques are used to test market efficiency while permitting the presence of risk premia. Five commodity markets were tested at the eight and twenty-four week horizon. Results showed that all five were sometimes inefficient but no market was inefficient always. Moreover, rejections of the unbiasedness hypothesis were nearly always caused by market inefficiency rather than the presence of risk premia.