We incorporate three important aspects of current climate policy, unilateralism, demand side approach and a climate target, in a multi-country model with flow dependent fossil fuel extraction costs and a backstop. It turns out that the optimal climate coalition should encompass all countries which are concerned about global warming and that the carbon tax increases initially to approach zero later on. While a fast increasing tax may cause an increase of early fossil fuel extraction (weak green paradox), a sufficiently large climate coalition can guarantee the adherence to the climate target. We present both a sufficient coalition size rule and the stable coalition size evolution path. It is shown that the results are robust to a stock dependence of extraction costs.