It is often assumed that in order to avoid the most severe consequences of global anthropogenic climate change we have to preserve our existing carbon sinks, such as for instance tropical forests. Global carbon sink conservation raises a host of normative issues, though, since it is debatable who should pay the costs of carbon sink conservation, who has the duty to protect which sinks, and how far the duty to conserve one's carbon sinks actually extends, especially if it conflicts with other duties one might have. According to some, forested states like Ecuador have a duty to preserve their tropical forests while the rich states of the global North have a duty of fairness to compensate states like Ecuador for the costs they incur. My aim in this paper is to critically analyse this standard line of argument and to criticise its validity both internally (i.e. with regard to its normative conclusion based on its premises) and externally (i.e. with regard to the argument's underlying assumptions and its lack of contextualisation). As I will argue, the duty to conserve one's forests is only a particular instantiation of a wider, more general duty to contribute towards global climate justice for which the context in which one operates (e.g. whether other agents are complying with their duties of global climate justice or not) matters significantly.