Tensioned precision structures has been shown to have potentially greater passive stability, more deterministic dynamics, and simpler metrology requirements than those of the traditional truss structure, where structural stiffness is derived from the nonlinear geometric or stress stiffening of the tensioned structure, rather than from the mechanics of materials. With the absence of structural depth, the traditional design issues with thermal deformations are reduced to two-dimensions, and metrology and shape control may be simplified into the load management and planarity control of discrete tensioning points. The presented structure is based on a discretized membrane approach, composed of effectively rigid in-plane panels and tuned, complaint hinges, which are especially complaint in shear. This research investigates and reports the effect of shear compliance on the reduction of buckling or wrinkling within a tensioned structure, as well as, the implications of membrane discretization density on efficient and effective structural design. Generalized back-of-the-envelope models are used to identify critical design trades and limits in design feasibility.