A concise analysis of sixth-order perturbation theory and coupled cluster theory is presented, and several computational schemes correct through sixth order are constructed based upon an underlying coupled cluster singles and doubles calculation. The sixth-order corrections with respect to the coupled cluster singles and doubles wave function are identified and appropriate contributions are added to the energy using an n(9) algorithm. Depending upon the type of the initial functional, several computational approaches can be developed. All of the methods considered have been tested for several small molecules and the results compared to the exact values. An average error of 0.3 mhartree is achieved compared to 0.1 mhartree for CCSDTQ (coupled cluster singles, doubles, triples, and quadruples).