This paper discusses the optimal height-wise distribution of supplemental viscous dampers in multistorey building structures. Seismic excitation is modeled as stochastic stationary process and response statistics for linear structural systems are obtained through state-space analysis. For nonlinear damper applications statistical linearization is employed to accommodate a similar, state-space formulation. Emphasis is placed on three practical design issues: (i) realistic quantification of damper upfront cost based on damper force capacity rather than on the damping coefficient; (ii) investigation of bracing configuration schemes anchored at non-consecutive floor levels; and (iii) consideration of the cost of column strengthening required to accommodate the additional axial loads due to the supplemental damping system. Five different cost-based objective functions are defined to address these issues and the impact of each of them on the optimal damper distribution is examined in detail. Adjustments for estimation of peak responses when statistical linearization is used are also discussed. The optimal design problem considers the structural performance as a constraint, requiring that a target vibration suppression be achieved through the damper addition. An extension to a multi-objective design optimization is also discussed, incorporating the vibration suppression level as additional objective. The proposed approach is illustrated considering an actual Chilean 26-storey building subjected to an excitation compatible with the Chilean seismic hazard. Results show that damper distributions optimized considering realistic cost assessments are more efficient (with respect to cost-based design objectives) than distributions optimized considering simplified criteria. It is also demonstrated that consideration of practical issues such as column strengthening and feasible damper force capacity have a considerable influence on the optimal distribution. Finally, results also show that further cost reductions can be achieved with braces anchored at non-consecutive floor levels, and that such reductions are consistent with predictions given by approximate analytical expressions.