The environmental loads, such as wind and earthquake loads, possess many frequency components. Therefore, tuned mass dampers (TMDs) are optimized to render them effective for such large bandwidth inputs. To broaden the operational range of a TMD an external damper is introduced in the optimization procedure. Although this added damper smoothens the sharp peaks of frequency response function out of the operating range it also considerably decreases the effectiveness of TMD in the operating range. In this book an alternative approach is proposed where the response of the structure is constrained in the boundaries of the operating range of TMD. Then the requirement for additive damping could be eliminated and TMD can be used in full efficiency.