The BCS and/or HFB theories are extended by treating the effect of four quasi-particle states perturbatively. The approach is tested on the pairing hamiltonian, showing that it combines the advantage of standard perturbation theory valid at low pairing strength and of non-perturbative approaches breaking particle number valid at higher pairing strength. Including the restoration of particle number, further improves the description of pairing correlation. In the presented test, the agreement between the exact solution and the combined perturbative + projection is almost perfect. The proposed method scales friendly when the number of particles increases and provides a simple alternative to other more complicated approaches.