The possibility of a linear-creep (Newtonian-viscosity) upper mantle is reexamined on the basis of present knowledge on flow mechanisms in olivine, including differences between activation parameters for creep and for diffusion, and revised estimates of grain boundary width. Results of the comparison between linear superplastic creep and power-law creep are presented as crossover temperature between lattice and grain-boundary diffusion, and crossover stress between non-linear and linear creep, as a function of temperature (depth), grain size, grain-boundary width, grain-boundary diffusion activation energy, and rate-controlling species (silicon or oxygen). For the most realistic values of the parameters, linear creep is well within the range of possibilities. There is no major objection from rheology to the idea of a Newtonian-viscosity upper mantle. Viscosities for the two kinds of creep are compared for laboratory, upper mantle, and-tentatively-lower mantle conditions. This results in a prediction of the grain size at which Coble creep could be observed in olivine polycrystals in the laboratory (~ 10 μm or less). The upper mantle viscosity is in the 1020-1021 Pa s range. Minimum estimates for the viscosity of the lower mantle are of the same order. The pictures of the rheology of the mantle derived from microphysical models of flow and from geophysical observation can therefore be made compatible.