We examine the implications for the viability of multilateral cooperation of different legal principles governing how separate international agreements relate to each other. We contrast three alternative rules: conditionality - making cooperation in one area a condition for cooperation in another; separation - forbidding sanctions in one area to be used to enforce cooperation in others; and open rules, i.e., the absence of any restriction on the patterns of cross-issue cooperation arrangements and sanctions. As an example, we focus on trade and environmental agreements. Our analysis suggests that conditionality is more likely to facilitate multilateral, multi-issue cooperation in situations where the environmental policy stakes are small relative to the welfare effects of trade policies; when the costs of environmental compliance are high, a conditionality rule can hinder multilateral cooperation. Separation can undermine cooperation by limiting punishment, but can also promote broad cooperation by making partial cooperation more difficult to sustain.