At NLR a system for the computational design on multi-element airfoil has been developed. This design system solves the inverse aerodynamic problem in an approximate way. A priori specified aerodynamic requirements (surface pressure distribution) and geometric requirements are minimized in a least-squares way, introducing weight factors to emphasize locally either the aerodynamic or the geometric requirements. With the objective to evaluate the capabilities of the design tool it has been applied to a two-element airfoil. The starting configuration was a wing with slat tested earlier in the wind tunnel, exhibiting rather unfavourable drag characteristics. The design has been focussed on the wing nose geometry at the slat intersection. To improve the drag characteristics a target pressure distribution was defined with a reduced suction level on the wing nose. The computations indicated that this target could be achieved with satisfactory approximation (fulfilling at the same time a set of geometry requirements). This was confirmed by measurements in the wind tunnel. The tests also showed that a substantial drag reduction was achieved with the newly designed wing nose.