Strategies of reducing the number of bars of a sparse plate-truss, while increasing structural height and improving structural performance are considered. Four strategies are presented by considering seven plate-trusses. The morphological and structural properties of each of the plate trusses with reduced number of bars are discussed. An approximate and quick method to find the stiffness coefficients of a periodic unit of the plate-truss is presented and an equivalent single stiffness coefficient is introduced. The stiffness coefficients enable the designer to understand the existing relationship between the morphology of a truss and its structural ability. They are very useful for a comparison of structural ability of different sparse-trusses and permit a determination of the relative structural efficiency of each strategy of reducing the bar density.