It has been argued recently that the combination of risk aversion and an uncertainty distribution of future temperature change with a heavy upper tail invalidates mainstream economic analyses of climate change policy. A simple model is used to explore the effect of imposing an upper bound on future temperature change. The analysis shows that imposing even a high bound reverses the earlier argument and that the optimal policy, as measured by the willingness to pay to avoid climate change, is relatively insensitive to this bound over a wide range.