Seismic-frequency torsional forced-oscillation measurements of shear modulus dispersion and associated strain-energy dissipation under conditions of simultaneously high temperature and pressure in our laboratory require the specimen to be enclosed within a thin-walled metal sleeve – typically of mild steel. However, the well-known transition between the austenite and ferrite phases on cooling across the interval 900-700ºC complicates its mechanical behaviour. The resulting uncertainty tends to mask the seismologically important onset, within this temperature range, of appreciably anelastic behaviour of polycrystalline olivine. In order to more closely document this important transition in mechanical behaviour, we have conducted an unpublished study in which of a specimen of polycrystalline olivine is jacketed within a copper sleeve which retains its face-centred-cubic (fcc) structure throughout the range of the measurements limited to 1050ºC by the proximity of the melting point. Here we report measurements to higher temperature (1200ºC) in which we employ austenitic (fcc) stainless steel (SS) as an alternative jacket material. Two parallel reference experiments with a SS-jacketed SS specimen and a SS-jacketed sapphire specimen were also conducted to obtain the mechanical properties of the jacket material. Such information concerning the viscoelastic behaviour of SS is used to subtract the torsional stiffness of the SS jacket from the properties of SS-jacketed olivine and thereby isolate the mechanical behaviour of olivine. The resulting dissipation spectrum for the olivine specimen consists of a monotonic background dissipation with a superimposed peak located within the 1-1000 s period range for temperatures between 900 and 1050ºC. The dissipation peak and associated shear modulus dispersion, potentially attributable to elastically accommodated grain boundary sliding, display an Arrhenius dependence upon temperature - moving systematically to shorter periods with increasing temperature. Comparison of the results obtained for sol-gel Fo₉₀ olivine specimens enclosed within the alternative mild-steel, copper, and stainless-steel jackets will provide new insight into the nature of the seismologically important transition between the elastic and anelastic regimes.