A system for wave resistance minimisation of ship hull forms has been developed before. It uses surrogatebased global optimisation, with hull form variations by a parametric blending of basis hull forms; and wave resistance calculation by a potential flow solver. This procedure is briefly summarised. The paper then describes a study on the use of a similar system together with a free-surface RANS solver, for minimisation of the stern wave system. Multiobjective optimisation for the stern of a slender ship at 2 speeds is performed. Multi-fidelity methods, with response surfaces based on a dense set of potentialflow results and a coarse set of RANS data, are applied and compared with the single-fidelity formulation. The response surfaces and their dependence on the number of high-fidelity data points are studied. The multifidelity methods appear to hold promise for a reduction of the required number of high-fidelity computations. For the present case, the potential-flow solver already was quite accurate; further studies for less slender hull forms, to get a clearer view of the actual advantage of multi-fidelity methods in practice, are in progress.