A method for finding the optimum alloy compositions considering a large number of property requirements and constraints by systematic exploration of large composition spaces is proposed. It is based on a numerical multi-criteria global optimization algorithm (multistart solver using Sequential Quadratic Programming), which delivers the exact optimum considering all constraints. The CALPHAD method is used to provide the thermodynamic equilibrium properties, and the creep strength of the alloys is predicted based on a qualitative numerical model considering the solid solution strengthening of the matrix by the elements Re, Mo and W and the optimum morphology and fraction of the. gamma'-phase. The calculated alloy properties which are required as an input for the optimization algorithm are provided via very fast Kriging surrogate models. This greatly reduces the total calculation time of the optimization to the order of minutes on a personal computer. The capability of the multicriteria optimization method developed was experimentally verified with two new single crystal superalloys. Their compositions were designed such that the content of expensive elements was reduced. One of the newly designed alloys, termed ERBO/13, is found to possess creep strength of only 14 K below CMSX-4 in the high-temperature/low-stress regime although it is a Re-free alloy.