This paper concerns optimal emissions of greenhouse gases when catastrophic consequences are possible. A numerical model is presented which takes into account both continuous climate-feedback damages as well as the possibility of a catastrophic outcome. The uncertainty in the model concerns whether or not a future catastrophe will occur. However, the welfare losses imposed by such an outcome are assumed known to the decision-maker. An important result is that the possibility of a climate catastrophe is a major argument for greenhouse gas abatement even in absence of continuous damage. Special attention is given to analyses on the probability of a catastrophe and the pure rate of time preferences, and the implicit values of these parameters are calculated if the Rio stabilisation target is assumed to be optimal. Finally, the expected value of perfect information about the probability of the arrival of a catastrophe is estimated.