This paper investigates the effects of mass/stiffness ratio between stories with and without dampers, and the stories ratio on the Ds-value, which expresses the response-reduction effect, and the dampers’ energy absorption for a medium/low-rise building, aiming to contribute to the actual design of vibration control structures with dampers installed in partial stories. It also determines realistic constraints on the maximum shear coefficient and the maximum inter-story deformation angle of a 1-layer with respect to the design input energy, and propose a simple practical formula for the primary natural period of a main frame that copes with these constraints.