An innovative application of Direct Displacement-Based Design (DBD) is presented for a modern 8-storey dual system structure consisting of interior concrete walls in parallel to a number of large steel eccentrically braced frames, fitted with visco-elastic dampers at link positions. The innovative DBD methodology lets the designer directly control the forces in the structure by choosing strength proportions at the start of the design procedure. The strength proportions are used to establish the displaced shape at peak response and thereby establish the equivalent single-degree-of-freedom system design displacement, mass and effective height. A new simplified formulation for the equivalent viscous damping of systems possessing viscous dampers is proposed which also utilises the strength proportions chosen by the designer at the start of the process. The DBD approach developed is relatively quick to use, enabling the seismic design of the 8-storey case study structure to be undertaken without the development of a computer model. To verify the ability of the design method, non-linear time-history analyses are undertaken using a suite of spectrum-compatible accelerograms. These analyses demonstrate that the design solution successfully achieves the design objectives to limit building deformations, and therefore damage.