This paper uses cointegration procedures to test for agricultural commodity futures market efficiency in the UK. Cointegration between spot and futures prices is a necessary condition for market efficiency where these prices are characterised by stochastic trends (Lai and Lai 1991). In addition, acceptance of the 'unbiasedness hypothesis' requires that the spot and lagged futures prices are cointegrated with the cointegrating vector (1, -1). Alternatively, Brenner and Kroner (1995) use a no-arbitrage cost-of-carry model to argue that the existence of cointegration between spot and futures prices depends on the time series properties of the cost-of-carry. According to Brenner and Kroner (1995), a tri-variate cointegrating relationship (the BK hypothesis) should exist among the spot price, the lagged futures price and the lagged interest rate (that component of cost-of-carry most likely to be non-stationary). These variables should be cointegrated with a cointegrating vector (1, -1, 1). Kellard (2002) finds that both bi-variate and tri-variate cointegrating relationships are found in a sample from the wheat futures market in the UK, and thus the so-called "cointegration paradox" emerges. As Kellard (2002) points out this paradox exists because it is theoretically impossible for two variables to be cointegrated with each other while simultaneously being cointegrated with a third variable. Using a larger sample of wheat futures market prices from LIFFE both the 'unbiasedness hypothesis' and the 'BK hypothesis' are examined. The results indicate that the 'BK hypothesis' should be rejected.