Using statistical emulators to guide sequential evaluations of complex computer experiments is now a well-established practice. When a model provides multiple outputs, a typical objective is to optimize one of the outputs with constraints (for instance, a threshold not to exceed) on the values of the other outputs. We propose here a new optimization strategy based on the stepwise uncertainty reduction paradigm, which o ers an e cient trade-off between exploration and local search near the boundaries. The strategy is illustrated on numerical examples.