In this work we reconsider the strongly contracted variant of the n-electron valence state perturbation theory (SC NEV-PT) which uses Dyall's Hamiltonian to define the zero-order energies (SC NEV-PT(D)), We develop a formalism in which the key quantities used for the second-order perturbation correction to the energy are written in terms of the matrix elements of suitable operators evaluated on the zero-order wavefunction, without the explicit knowledge of the perturbation functions. The new formalism strongly improves the computation performances. As test cases we present two preliminary studies: (a) on N-2 where the convergence of the spectroscopic properties as a function of the basis set and CAS-CI space is discussed and (b) on Cr-2, where it is shown that the SC NEV-PT(D) method is able to provide the correct profile for the potential energy curve.