Na and Shin showed that the ‘veil of uncertainty’ can be conducive to the success of self-enforcing international environmental agreements. Later papers confirmed this conclusion about the negative impact of learning. In the light of intensified research efforts worldwide to reduce uncertainty about the environmental impact of emissions and the cost of reducing them, this conclusion is intriguing. The purpose of this paper is threefold. First, we analyse whether the result carries over to a more general setting without restriction on the number of players and which considers not only ‘no’ and ‘full learning’ but also ‘partial learning’. Second, we test whether the conclusion also holds if there is uncertainty about abatement costs instead of uncertainty about the benefits from global abatement. Third, we propose a transfer scheme that mitigates the possible negative effect of learning and which may even transform it into a positive effect.