Many countries adjust their trade policies countercyclically with food prices, to the extent that the use by numerous food exporters of export restrictions has occasionally threatened the food security of food importing countries. These trade policies are inconsistent with the terms-of-trade motivation often retained to characterize the payoff frontier of self-enforcing trade agreements, as they can worsen the terms of trade of the countries that apply them. This paper analyzes trade policy coordination when trade policies are driven by terms-of-trade effects and a desire to reduce domestic food price volatility. This framework implies that importing and exporting countries have incentives to deviate from cooperation at different periods: the latter when prices are high and the former when prices are low. Since staple food prices tend to have asymmetric distributions, with more prices below than above the mean but with occasional spikes, a self-enforcing agreement generates asymmetric outcomes. Without cooperation, an importing country uses more frequently its trade policy because of the concentration of prices below the mean, but an exporting country has a greater incentive to deviate from a cooperative trade policy because positive deviations from the mean price are larger than negative ones. Thus, the asymmetry of the distribution of commodity prices can make it more difficult to discipline export taxes than tariffs in trade agreements.