This paper compares optimal results that are based on the solution of Riccati equation with optimal results achieved by an analysis/redesign optimization scheme. Two examples of framed structures are considered: a 3 story shear frame excited by a single record and a 10 story industrial frame excited by an ensemble of 20 ground motions. The added damping for each of the structures is designed using each of the two methods such that the total added damping is equal for both. A time history analysis for the whole ensemble is carried out to yield the envelope of maximal inter-story drifts and their mean for all records. It is shown that the results of the analysis/redesign schemes are superior, in the practical sense, with respect to the Riccati based design.