This work studies tensegrity bracing systems to be used as energy dissipation devices in next generation, earthquake-proof timber buildings. The examined lightweight and high-strength structures with re-centering capabilities are formed by timber members and pretensioned elements with a superelastic response, which may consist of shape memory alloy wires, cables or bars with energy dissipation capacity. In the case of bars, we assume that such members can be protected against buckling through their encasement in buckling-restrained devices, so as to respond both in tension and in compression. The work on the analyzed bracing systems presents novel results on this type of bi-directional response and the effects derived from the pretension of the superelastic elements, within an analytic formulation of the mechanical response of the structure. It includes an example dealing with a full-scale glued laminated timber frame, which compares the responses of different bracing systems in terms of the lateral force vs. drift ratio curve and ductility factor. The beneficial effects deriving from the use of buckling-restrained devices in an inverted V-braced timber frame are discussed. The presented results highlight the high potential of superelastic braces with tensegrity architecture for the design of timber frames exhibiting markedly high ductility ratios, which considerably surpass those of full-timber or timber-steel systems.