A methodology for the numerical treatment of a two-objective minimization problem, possibly subject to equality constraints is proposed. Such a problem is a basic step in multidisciplinary optimization, sometimes referred to as concurrent engineering. Here, we consider the case where one criterion to be minimized, J_A , is preponderant over the second, J_B , that is, either more critical or more fragile. The problem is formulated as a parametric optimization in which the two criteria are smooth functions of a common design vector Y ∈ R^N . The numerical procedure is made in two steps.