The starting point of this paper is a climate coalition which seeks to reduce global emissions. It is well known from the literature on (spatial) carbon leakage that the climate effect of unilateral measures may be partly offset by the actions of the free-riders. Furthermore, from the literature on the green paradox, we know that stringent demand-side policies in the future may increase present emissions. The novelty of this paper is that we also explore how the coalition's future policies regarding own fossil fuel production (supply-side policies) affect the present emissions from the free-riders. In particular, we find that a credible announcement of future unilateral supply-side policies reduces early foreign emissions. We derive the optimal combination of consumer taxes and producer taxes when both spatial and intertemporal leakages from the free-riders are taken into account. We show that the tax shares generally differ over time, and that a declining present value of the social cost of carbon over time supports a time path where the consumer tax's share of the total carbon tax also declines over time. We illustrate our findings with a numerical model for the global fossil fuel markets, considering European unilateral carbon policies.