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Hierarchical, nano-twinned microstructures are a promising route to optimize the strength and deformability of metals and alloys. The present paper investigates the role of grain and twin boundaries and the effect of twin spacing on the evolution of plasticity in a twinned, polycrystalline γ-TiAl microstructure. Via atomistic simulations of uniaxial compression tests it is possible to disentangle these influencing factors, and the results show that the onset of plasticity is governed by the sub-grain structure of the samples, while the Schmid factor does not play a prominent role. At high strains in uniform or only slightly twinned models, grain boundary sliding is one of the major deformation mechanisms, whereas twin-boundary-mediated plastic deformation dominates the highly twinned structures. Moreover, based on analyzing the degree of localization parameter, it is inferred that upon decreasing the lamellae size, higher uniformity of shear strain in the samples can be achieved. These results can be used to inform mesoscale numerical modeling of hierarchical TiAl microstructures.