Height-wise distributions of viscous dampers for the optimal reduction of peak floor accelerations in multi-story buildings subjected to earthquakes are obtained. The effects of the fundamental period, the frequency content of the seismic excitation, the number of stories, and the velocity exponent of the dampers are also investigated. The seismic excitation is modeled as a non-stationary stochastic process and the stochastic structural response is obtained by the Explicit Time Domain method. Optimal damper distributions are found using zero-order optimization algorithms. Sub-optimal solutions that minimize the amount of added damping to produce a response reduction constrained to a fraction of the optimal reduction are also explored. The effects of the optimized damper distributions on other response quantities are also assessed. The optimized solutions are validated by a case study that considers a realistic structure subjected to actual seismic ground motions. It is found that the optimal reduction of peak floor accelerations depends mainly on the relationship between the fundamental period of the structure and the frequency content of the seismic excitation. It is also found that sub-optimal solutions are more convenient than optimal solutions in the sense that they require smaller (much smaller in many cases) amounts of supplemental damping to achieve response reductions that are just slightly smaller than the optimal reductions. Finally, it is observed that damper distributions optimized solely for the reduction of the peak floor acceleration response also lead to significant reductions in other relevant response quantities such as inter-story drift and base shear.