Controversy surrounds climate change policy analyses because of uncertainties in climatic effects, impacts, mitigation costs and their distributions. Here we address uncertainties in impacts, and provide a method for quantitative estimation of the policy implications of such uncertainties. To calculate an "optimal" control rate or carbon tax a climate-economy model can be used on estimates of climate damages resulting from warming scenarios and several other key assumptions. The dynamic integrated climate-economy (DICE) model, in its original specification? suggested that an efficient policy for slowing global warming would incorporate only a relatively modest amount of abatement of greenhouse gas emissions, via the mechanism of a small (about $5 per ton initially) carbon tax. Here, the DICE model is reformulated to reflect several alternate published estimates and opinions of the possible damages from climatic change. Our analyses show that incorporating most of these alternate damage estimates into DICE results in a significantly more aggressive optimal policy than that suggested by the original model using a single damage function. In addition, statistical distributions of these damage estimates are constructed and used in a probabilistic analysis of optimal carbon tax rates, resulting in mostly much larger (but occasionally smaller) carbon taxes than those of DICE using point values of damage estimates. In view of the large uncertainties in estimates of climate damages, a probabilistic formulation that links many of the structural and data uncertainties and thus acknowledges the wide range of "optimal" policies is essential to policy analysis, since point values or "best guesses" deny policy makers the opportunity to consider low probability, but policy-relevant, outliers. Our presentation is offered as a prototypical example of a method to represent such uncertainties explicitly in an integrated assessment.