The first high-temperature mechanical spectroscopy experiments on high-purity polycrystalline MgO reveal a monotonically frequency-and temperature-dependent dissipation 'background'-without any evidence of the superimposed dissipation peak observed in a previous study of a specimen of lower-purity [Webb, S. and Jackson, I. Phys. Chem. Min., 2003 30, 157]. The dissipation and associated relaxation of the shear modulus observed in both studies are well described in an internally consistent manner by a novel Burgers-type model based on a creep function incorporating suitable distributions of anelastic relaxation times. The contrasting patterns for the two materials reinforce an emerging generalisation concerning high-temperature viscoelastic behaviour, whereby the presence of a secondary intergranular phase of relatively low viscosity, and the associated rounding of grain edges, is apparently required to allow elastically accommodated grain-boundary sliding. The absence, in sufficiently pure polycrystalline materials, of a dissipation peak attributable to elastically accommodated grain-boundary sliding is in conflict with classical micromechanical models for grain-boundary sliding, which are therefore being revisited.