This paper presents an illustrative example of the advantages offered by inserting added viscous dampers into shear-type structures in accordance with a special scheme based upon the mass proportional damping (MPD) component of the Rayleigh viscous damping matrix. In previous works developed by the authors, it has been widely shown that, within the class of Rayleigh damped systems and under the "equal total cost" constraint, the MPD system provides best overall performance both in terms of minimising top-storey mean square response to a white noise stochastic input and maximising the weighted average of modal damping ratios. A numerical verification of the advantages offered by the application of MPD systems to a realistic structure is presented herein with reference to a 4-storey reinforced-concrete frame. The dynamic response of the frame subjected to both stochastic inputs and several recorded earthquake ground motions is here analysed in detail. The results confirm the good dissipative properties of MPD systems and indicate that this is achieved at the expense of relatively small damping forces.