Several studies found ancillary benefits of the provision of public goods to be of considerable size. If these additional private benefits were noticed, they would imply not only higher cooperative but also non-cooperative provision levels. However, beyond these largely undisputed important quantitative effects, there would be qualitative and strategic implications associated with ancillary benefits: public policy would no longer be a pure but an impure public good. In this paper, we investigate these implications in a setting of non-cooperative coalition formation in the context of climate change. In particular, we address the following question. Would ancillary benefits if they were taken in consideration increase participation in international climate agreements and raise the success of these treaties in welfare terms?