This paper studies uncertainty about the non-linearity of climate change impact. The DIAM 2.3 model is used to compute the sensitivity of optimal CO2 emissions paths with respect to damage function parameters. This builds upon results of the EMF-14 uncertainty subgroup study by explicitly allowing for the possibility of threshold effects and hockey stick damage functions. It also extends to the cost-benefits framework previous studies about inertia of energy systems. Results show that the existence of a threshold in the damage function is critical to precautionary action. Optimal path are much less sensitive to uncertainty on the scale of the damages than on the threshold values.