We investigate basis set reduction (BSR), a configuration-based multi-reference perturbation theory using an implicit effective Hamiltonian motivated by Brillouin-Wigner perturbation theory. This approach avoids the intruder-state and level-crossing problems by construction and yields a rapidly converging perturbation expansion. Formulated to systematically approximate multi-reference configuration interaction, BSR yields accurate results in second order, because it includes relaxation effects of the primary space wavefunction in the presence of the perturbation. We benchmark the method for molecules (CH2,O-3) in which both dynamical and non-dynamical correlation effects are known to be important, obtaining accuracies of the order of 1 kcal/mol across the potential energy surface in second-order perturbation theory. We address the critical issues of perturbative orbital optimization for the primary orbital space, the choice of the secondary orbital space and the effects of single excitations.