Solar geoengineering has received increasing attention as an option to temporarily stabilize global temperatures. A key concern is that heterogeneous preferences over the optimal amount of cooling combined with low deployment costs may allow the country with the strongest incentive for cooling, the so-called free-driver, to impose a substantial externality on the rest of the world. We analyze whether the threat of counter-geoengineering technologies capable of negating the climatic effects of solar geoengineering can overcome the free-driver problem and tilt the game in favour of international cooperation. Our game-theoretical model of countries with asymmetric preferences allows for a rigorous analysis of the strategic interactionsurrounding solar geoengineering and counter-geoengineering. We find that counter-geoengineering prevents the free-driver outcome, but not always with benign effects. The presence of counter-geoengineering leads to either a climate clash where countries engage in a non-cooperative escalation of opposing climate interventions (negative welfare effect), a moratorium treaty where countries commit to abstain from either type of climate intervention (indeterminate welfare effect), or cooperative deployment of solar geoengineering (positive welfare effect). We show that the outcome depends crucially on the degree of asymmetry in temperature preferences between countries.