Damping layers, widely used for noise and vibration control of thin-walled structures, can be designed to provide an optimal trade-off between performance and weight which is of particular importance in the automotive and aircraft industry. The goal of the presented work is the minimization of sound power radiated from plates under broadband excitation by redistribution of unconstrained damping layers. The total radiated sound power is assumed to be represented by the sound power radiated at the structural resonances. Resonance tracking is performed by means of single-degree-of-freedom (SDOF)-approximations based on near-resonance responses and their frequency derivatives. Axisymmetric vibrations of circular plates under several boundary and forcing conditions are considered. Frequency dependent Young's modulus and loss factor of the damping material are taken into account. Vibration analysis is based on the finite element method (FEM) while acoustic radiation is treated by means of Rayleigh's integral formula. It is shown that, starting from a uniform damping layer distribution, substantial reductions in radiated sound power can be achieved through redistribution of the damping layers. Depending on the given situation, these reductions are not only due to amplitude reductions but also to changes in vibration shapes and frequencies.