We consider multi-objective optimization problems, min x∈Rd(f1(x), . . . , fm(x)), where the functions are expensive to evaluate. In such a context, Bayesian methods relying on Gaussian Processes (GP) [1], adapted to multi-objective problems [2] have allowed to approximate Pareto fronts in a limited number of iterations. In the current work, we assume that the Pareto front center has already been attained (typically with the approach described in [3]) and that a computational budget remains. The goal is to uncover of a broader central part of the Pareto front: the intersection of it with some region to target, IR(see Fig. 1). IR has however to be defined carefully: choosing it too wide, i.e. too ambitious with regard to the remaining budget, will lead to a non converged approximation front. Conversely, a suboptimal diversity of Pareto optimal solutions will be obtained if choosing a too narrow area. The GPs allow to forecast the future behavior of the algorithm: they are used in lieu of the true functions to anticipate which inputs/outputs will be obtained when targeting growing parts of the Pareto front. Virtual final Pareto fronts corresponding to a possible version of the approximation front at the depletion of the budget are produced for each IR. A measure of uncertainty is defined and applied to all of them to determine the optimal improvement region IR∗, balancing the size of the approximation front and the convergence to the Pareto front.