The mineral olivine dominates the composition of the Earth's upper mantle and hence controls its mechanical behaviour and seismic anisotropy. Experiments at high temperature and moderate pressure, and extensive data on naturally deformed mantle rocks, have led to the conclusion that olivine at upper-mantle conditions deforms essentially by dislocation creep with dominant  slip. The resulting crystal preferred orientation has been used extensively to explain the strong seismic anisotropy observed down to 250 km depth. The rapid decrease of anisotropy below this depth has been interpreted as marking the transition from dislocation to diffusion creep in the upper mantle. But new high-pressure experiments suggest that dislocation creep also dominates in the lower part of the upper mantle, but with a different slip direction. Here we show that this high-pressure dislocation creep produces crystal preferred orientations resulting in extremely low seismic anisotropy, consistent with seismological observations below 250 km depth. These results raise new questions about the mechanical state of the lower part of the upper mantle and its coupling with layers both above and below.