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 μm 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 V_S, and the dissipation of shear strain energy Q⁻¹ have been measured as functions of oscillation period T_o, 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 < T_o < 100 s, by the expression Q⁻¹ = A [T_od⁻¹ exp (−E/RT)]^α with A = 7.5 × 10² s^−α μm^α, 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 T_o. 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 V_S is increased substantially by the viscoelastic relaxation allowing the lateral variability of wave speeds to be associated with relatively small temperature perturbations.