Within the frame of second-order multi-reference perturbation theory (MR-PT), drawing on previous work of Dyall, a new partition of the Hamiltonian, which can loosely be considered as intermediate between Moller-Plesset (MP) and Epstein-Nesbet (EN), is presented. The method, which is well suited for CAS-SCF zero-order wavefunctions, is expected to correct partially the defects of MP and EN while retaining their good properties. The new approach has been successfully applied to some test cases involving the homonuclear diatomics F-2, Cl-2 and N-2 where the faults of the EN treatment appear to be in large measure eliminated. Application to the Cr, diatomic shows that the dramatic intruder state problem suffered by the MP treatment is completely solved, affording a qualitatively good description of the potential energy curve for the ground state.