Tensioned marine risers are often linked to the subsea wellhead or manifold by a stressjoint. This joint must have sufficient flexibility to keep the stresses in the riser end at an acceptable level, but still strong enough to resist the forces introduced from the riser. In the present paper this design problem is handled as a minimization problem, using the stressjoint volume as the function to minimize; some geometry parameters as free variables, and maximum allowable stresses as restrictions, A design procedure is established by combined use of one program for global response analysis of the riser, another program for detailed stress analysis of the joint, and finally computer code for nonlinear optimization. This tool has been applied in a case study where the performance of steel and titanium joints has been compared, The conclusion is that titanium joints will be significantly smaller than steel joints; they will be more robust when subjected to loads in excess of the design loads, and they will reduce the moment transmitted to the wellhead significantly.