Solar geoengineering (SG), also known as solar radiation management, has received increasing attention as an option to temporarily stabilise global temperatures. A key concern surrounding these technologies is of a strategic nature: International anarchy, heterogeneous preferences over the optimal amount of cooling, and low deployment costs may allow the country (or the bloc of countries) with the strongest incentive for cooling, the so-called free driver, to impose a substantial externality on the rest of the world. We analyse whether the threat of counter-geoengineering (CG), in the form of neutralising particles or potent greenhouse gases, can overcome the free driver problem and tilt the game in favor of cooperation. Our game-theoretical model of asymmetric countries allows a rigorous analysis of the strategic interaction surrounding SG and CG, confirming that the free driver outcome becomes unstable once CG is available. The possibility of CG can lead to a technological arms race (negative welfare effect), a moratorium (indeterminate welfare effect), but it can also lead countries to cooperate (positive welfare effect). Ultimately, the outcome depends on the level of asymmetry between countries.