We present the first application of the Rayleigh-Ritz variational procedure to the coupled cluster doubles trial function. The variational approach is applied to the potential surface of H-4, the double dissociation of water and the dissociation of N-2, and the results are compared to standard coupled cluster doubles calculations. It is found that the variational approach gives a greatly improved description of strongly correlated systems, where the standard approach is known to fail. Some examination of the basis set dependence of the results is presented.