Despite the growing concern about actual on-going climate change, there is little consensus about the scale and timing of actions needed to stabilise the concentrations of greenhouse gases. Many countries are unwilling to implement effective mitigation strategies, at least in the short-term, and no agreement on an ambitious global stabilisation target has yet been reached. It is thus likely that some, if not all countries, will delay the adoption of effective climate policies. This delay will affect the cost of future policy measures that will be required to abate an even larger amount of emissions. What additional economic cost of mitigation measures will this delay imply? At the same time, the uncertainty surrounding the global stabilisation target to be achieved crucially affects short-term investment and policy decisions. What will this uncertainty cost? Is there a hedging strategy that decision makers can adopt to cope with delayed action and uncertain targets? This paper addresses these questions by quantifying the economic implications of delayed mitigation action, and by computing the optimal abatement strategy in the presence of uncertainty about a global stabilisation target (which will be agreed upon in future climate negotiations). Results point to short-term inaction as the key determinant for the economic costs of ambitious climate policies. They also indicate that there is an effective hedging strategy that could minimise the cost of climate policy under uncertainty, and that a short-term moderate climate policy would be a good strategy to reduce the costs of delayed action and to cope with uncertainty about the outcome of future climate negotiations. By contrast, an insufficient short-term effort significantly increases the costs of compliance in the long-term.