A realistic prototype high-rise building was designed and modeled using linear elastic (and also nonlinear) degrading stiffness idealizations. Using an effective damper mass ratio of 0.026, three different techniques were used to design an optimum tuned-mass damper (TMD) for the prototype. All were found to give essentially the same design. The response of the idealized prototype building to a strong ground motion was computed with and without a TMD. The TMD did not reduce the prototype's maximum response. Based on these results, vibration absorbers do not seem effective in reducing the maximum seismic response of tall buildings.