In order to investigate the processes responsible for the attenuation of seismic shear waves in the Earth's upper mantle, four olivine polycrystals ranging in mean grain size d from 3 to 23 ¿m have been fabricated, characterized, and mechanically tested in torsion at high temperatures and seismic frequencies. Both the shear modulus, which governs the shear wave speed VS, and the dissipation of shear strain energy Q-1 have been measured as functions of oscillation period To, temperature T, and, for the first time, grain size. At sufficiently high T all four specimens display similar absorption band viscoelastic behavior, adequately represented for 1000 < T < 1200 or 1300¿C and 1 < To < 100 s, by the expression Q-1 = A <Tod-1 exp (-E/RT)>α with A = 7.5 ¿ 102 s-α ¿mα, α = 0.26 and E = 424 kJ mol-1. This mildly grain-size-sensitive viscoelastic behavior of melt-free polycrystalline olivine is attributed to a combination of elastically and diffusionally accommodated grain boundary sliding, the latter becoming progressively more important with increasing T and/or To. Extrapolation to the larger (mm-cm) grain sizes expected in the Earth's upper mantle yields levels of dissipation comparable with those observed seismologically, implying that the same grain-size-sensitive processes might be responsible for much of the observed seismic wave attenuation. The temperature sensitivity of VS is increased substantially by the viscoelastic relaxation allowing the lateral variability of wave speeds to be associated with relatively small temperature perturbations.