Although climate models have steadily improved their ability to reproduce the observed climate, over the years there has been little change to the wide range of sensitivities exhibited by different models to a doubling of atmospheric CO2 concentrations. Stochastic optimization is used to mimic how six independent climate model development efforts might use the same atmospheric general circulation model, set of observational constraints, and model skill criteria to choose different settings for parameters thought to be important sources of uncertainty related to clouds and convection. Each optimized model improved its skill with respect to observations selected as targets of model development. Of particular note were the improvements seen in reproducing observed extreme rainfall rates over the tropical Pacific, which was not specifically targeted during the optimization process. As compared to the default model sensitivity of 2.4C, the ensemble of optimized model configurations had a larger and narrower range of sensitivities around 3C but with different regional responses related to the uncertain choice in optimized parameter settings. These results suggest current generation models, if similarly optimized, may become more convergent in their measure of global sensitivity to greenhouse gas forcing. However, this exploration of the possible sources of modeling and observational uncertainty is not exhaustive. The optimization process illustrates an objective means for selecting an ensemble of plausible climate model configurations that quantify a portion of the uncertainty in the climate model development process.