We propose a relaxation scheme for mathematical programs with equilibrium constraints (MPECs). In contrast to previous approaches, our relaxation is two-sided: both the complementarity and the nonnegativity constraints are relaxed. The proposed relaxation update rule guarantees (under certain conditions) that the sequence of relaxed subproblems will maintain a strictly feasible interior–even in the limit. We show how the relaxation scheme can be used in combination with a standard interior-point method to achieve superlinear convergence. Numerical results on the MacMPEC test problem set demonstrate the fast local convergence properties of the approach.