Worst-case design is important whenever robustness to adverse environmental conditions should be ensured regardless of their probability. It leads to minimax optimization, which is most often considered assuming that a closed-form expression for the performance index is available. In this paper, we consider the important situation where this is not the case and where evaluation of the performance index is via costly numerical simulations. In this context, strategies to limit the number of these evaluations are of paramount importance. This paper describes one such strategy, which further improves the performance of an algorithm recently presented that combines the use of a relaxation procedure for minimax search and Kriging-based efficient global optimization. Test cases from the literature demonstrate the interest of the approach.