Adding damping by the use of various damping devices has become an accepted method to reduce wind induced vibrations in tall buildings. An interesting example of a 39 story office tower is presented where large projected accelerations are the result of vortex shedding of an adjacent existing 52-story building. Viscous dampers and a toggle brace type motion amplification system are used to suppress the anticipated accelerations. A description of the damping system and its analytical simulation are discussed. This paper includes a nonlinear analysis of the tower, with time history forcing functions derived from wind tunnel testing. Cost data for the damper system is also presented.