A tuning experiment is carried out with the Community Atmosphere Model version 3, where the top-of-the-atmosphere radiative balance is tuned to agree with global satellite estimates from ERBE and CERES, respectively, to investigate if the climate sensitivity of the model is dependent upon which of the datasets is used. The tuning is done through alterations of cloud parameters that affect, for instance, the model cloud water content, but the difference in cloud water content between the two model configurations is found to be negligible compared to the wide spread of the same quantity in a number of state-of-the-art GCMs. The equilibrium climate sensitivities of the two model configurations differ by ca. 0.24 K, and both lie well within the range of present estimates of climate sensitivity in different GCMs. This indicates that it is possible to tune the model to either of the two satellite datasets without drastically changing the climate sensitivity. However, the study illustrates that the climate sensitivity is a product of choices of parameter values that are not well restricted by observations, which allows for a certain degree of arbitrariness in the estimates of climate sensitivity.