As an alternative to the environmental cartel approach, we assume that an international environmental agreement aims simply at providing a collective response to a perceived threat. Given this less demanding concept of cooperation and considering that most treaties become enforceable only after ratification by a sufficient number of participants, we examine the set of self-enforceable agreements. This set contains first-best but also second-best agreements that do not maximize the collective welfare of members but meet environmental and/or participative requirements. We study the properties of this set and discuss admissible values of targets and thresholds that favour economics over environmental objectives and vice versa.