Science and policy come together in the use of computer models for International Environmental Agreements (IEAs). We study a successful case in using Integrated Assessment Models (IAMs) in defining the long-range transboundary air pollution policies in Europe. In the light of the history of the LRTAP Convention of the UN-ECE, we consider the special circumstances which led to the success of the RAINS model that was employed. We find that the collaborative, self-aware and evolutionary character of the institutional framework built among the LRTAP Convention, IIASA and the EU facilitated the successful adoption of RAINS. We also show how the limits of computer models, fully recognised in this case by producers and users, leave issues of uncertainty, distribution and ethics unresolved. When facing international negotiations, several coalitions might emerge. An analysis of the situtation is done in terms of First-Comers and Late-Comers in Environmental policy, the first group undertaking the initiative to formulate international policies on issues that are of concern to themselves and for which they have acquired technologies, models and know-how, while the second group is just following international policy and most often viewing it as a constraint. This is discussed in the example of the Spanish participation in the negotiations about sulphur emissions in the buildup to the Oslo Protocol. The adoption of the precautionary principle is often being used as a way to handle uncertainty when facing urgent policy responsibilities for environmental issues.