Perturbed physics configurations of version 3 of the Hadley Centre Atmosphere Model (HadAM3) driven with observed sea surface temperatures (SST) and sea ice were tuned to outgoing radiation observations using a Gauss–Newton line search optimization algorithm to adjust the model parameters. Four key parameters that previous research found affected climate sensitivity were adjusted to several different target values including two sets of observations. The observations used were the global average reflected shortwave radiation (RSR) and outgoing longwave radiation (OLR) from the Clouds and the Earth's Radiant Energy System instruments combined with observations of ocean heat content. Using the same method, configurations were also generated that were consistent with the earlier Earth Radiation Budget Experiment results. Many, though not all, tuning experiments were successful, with about 2500 configurations being generated and the changes in simulated outgoing radiation largely due to changes in clouds. Clear-sky radiation changes were small, largely due to a cancellation between changes in upper-tropospheric relative humidity and temperature. Changes in other climate variables are strongly related to changes in OLR and RSR particularly on large scales. There appears to be some equifinality with different parameter configurations producing OLR and RSR values close to observed values. These models have small differences in their climatology with the one group being similar to the standard configuration and the other group drier in the tropics and warmer everywhere.