The optimum design of structures is obtained for three different types of damping treatments and the resulting designs are compared. The three types of damping treatments considered are constrained layer damping, active constrained layer damping and active damping. Piezoelectric material is used for actuators and sensors in the active damping and active constrained layer damping cases. The constraining layer of the active constrained layer damping case is the piezoelectric actuator. The structure is designed for minimum weight with constraints on the frequency and damping ratio. The problem is modeled using a two dimensional finite element based on the QUAD4 element. The QUAD4 element is modified to include viscoelastic and piezoelectric layers in the composite layup. The damping treatment is also allowed to move on the structure and to distort its shape so as to improve the damping characteristics of the initial design. Both beam and plate structures are considered to illustrate this concept. A proportional-derivative controller is used for the active control of the beam and the linear quadratic regulator (LQR) is used to design the active controller for the plates.