A rigorous perturbation theory is proposed, which has the same second order energy as the spin-component-scaled Møller-Plesset second order (SCS-MP2) method of Grimme [J. Chem. Phys. 118, 9095 (2003)]. This upgrades SCS-MP2 to a systematically improvable, true wave-function-based method. The perturbation theory is defined by an unperturbed Hamiltonian, Ĥ(0), that contains the ordinary Fock operator and spin operators Ŝ(2) that act either on the occupied or the virtual orbital spaces. Two choices for Ĥ(0) are discussed and the importance of a spin-pure Ĥ((0)) is underlined. Like the SCS-MP2 approach, the theory contains two parameters (c(os) and c(ss)) that scale the opposite-spin and the same-spin contributions to the second order perturbation energy. It is shown that these parameters can be determined from theoretical considerations by a Feenberg scaling approach or a fit of the wave functions from the perturbation theory to the exact one from a full configuration interaction calculation. The parameters c(os)=1.15 and c(ss)=0.75 are found to be optimal for a reasonable test set of molecules. The meaning of these parameters and the consequences following from a well defined improved MP method are discussed.