In the context of noise and vibration mitigation, passive damping treatments generally lead to low-cost and robust structural vibration control. In many engineering problems, constrained viscoelastic patches are added to the vibrating structure to increase the amount of damping. The efficiency of such damping treatments depends on the fraction of strain energy in the core layer and the inherent damping properties of the viscoelastic material. To design optimal damping treatments, the placement and the dimensions of the viscoelastic patches, as well as the material properties of the viscoelastic material must be optimised. The goal of this work if to present simple cost-effective techniques for the design of optimal constrained viscoelastic treatments.