We have extended cluster perturbation (CP) theory to comprehend the Lagrangian framework of coupled cluster (CC) theory and derived the CP Lagrangian energy series (L-CP) where the 2n + 1/2n + 2 rules for the cluster amplitudes and multipliers are used to get the energy corrections. We have also developed the variational CP (LCP) series, where the total cluster amplitudes and multipliers are determined through the same orders as in the L-CP series, but the energy is obtained by inserting the total cluster amplitudes and multipliers in the Lagrangian. The energies of the LCP series have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. With the exception of molecular systems that have a low lying doubly excited state compared to the electronic ground state configuration, we find that the fourth order models LCPS(D-4), LCPSD(T-4), and LCPSD(T-4) give energies of CC target state quality. For the LCPS(D-4) model, CC target state quality is obtained as the LCPS(D-4) calculation determines more than 99.7% of the coupled cluster singles and doubles (CCSD) correlation energy as the numerical deviations of the LCPS(D-4) energy from the CCSD energy were more than an order of magnitude smaller than the triples correlation contribution. For the LCPSD(T-4) and LCPSD(T-4) models, CC target state quality was obtained, given that the LCPSD(T-4) and LCPSD(T-4) calculations recover more than 99% of the coupled cluster singles doubles and triples (CCSDT) correlation contribution and as the numerical deviations of the LCPSD(T-4) and LCPSD(T-4) energies from the CCSDT energy were nearly and order of magnitude smaller than the quadruples correlation contribution. We, thus, suggest that the fourth order models may replace the full target CC models with no or very limited loss of accuracy. Published under an exclusive license by AIP Publishing.