Scanned, focused ultrasound systems (SFUS) have considerable flexibility in shaping the power deposition field during hyperthermia treatments. When utilizing this adaptability many complicated, interacting decisions must be made to obtain an optimal steady-state temperature distribution. This optimization problem is studied using a 3-D, radially symmetric simulation program which searches for a set of optimal scan parameters. The conjugate-gradient optimization technique with a golden section search was used to obtain the optimal temperature distributions attainable with a single circular scan of a tumour. The variable scan parameters of the single transducer heating system optimized (and under the control of the therapist) are: transducer tilt and rotation angles, focal depth, output acoustical power, and scan radius. This single scan study includes the effects of tumour and normal tissue blood perfusions, tumour depth, skin temperature boundary condition, as well as tumour size and shape. A similar, but less comprehensive, study was done for larger tumours using two concentric circular scans. The results show that (1) the optimization process can produce a set of scan parameters that give a considerably better temperature distribution than could be obtained ad hoc, and (2) the optimal scan parameter configuration obtained produces a close-to-ideal tumour temperature distribution for a wide variety of clinically relevant conditions. Thus, when extended to include data from individual patients such optimization should be a very useful tool in patient treatment planning, and should enhance the present capabilities of clinical scanned, focused ultrasound systems.