We demonstrate the application of an efficient multivariate probabilistic parameter estimation method to a spectral primitive equation atmospheric GCM. The method, which is based on the Ensemble Kalman Filter, is effective at tuning the surface air temperature climatology of the model to both identical twin data and reanalysis data. When 5 parameters were simultaneously tuned to fit the model to reanalysis data, the model errors were reduced by around 35% compared to those given by the default parameter values. However, the precipitation field proved to be insensitive to these parameters and remains rather poor. The model is computationally cheap but chaotic and otherwise realistic, and the success of these experiments suggests that this method should be capable of tuning more sophisticated models, in particular for the purposes of climate hindcasting and prediction. Furthermore, the method is shown to be useful in determining structural deficiencies in the model which can not be improved by tuning, and so can be a useful tool to guide model development. The work presented here is for a limited set of parameters and data, but the scalability of the method is such that it could easily be extended to a more comprehensive parameter set given sufficient observational data to constrain them.