  We report on a mechanism which may lead to a spin-up of the surface of a
rotating single star leaving the Hayashi line, which is much stronger than the
spin-up expected from the mere contraction of the star. By analyzing rigidly
rotating, convective stellar envelopes, we qualitatively work out the mechanism
through which these envelopes may be spun up or down by mass loss through their
lower or upper boundary, respectively. We find that the first case describes
the situation in retreating convective envelopes, which tend to retain most of
the angular momentum while becoming less massive, thereby increasing the
specific angular momentum in the convection zone and thus in the layers close
to the stellar surface. We explore the spin-up mechanism quantitatively in a
stellar evolution calculation of a rotating 12 M_sun star, which is found to be
spun up to critical rotation after leaving the red supergiant branch. We
discuss implications of this spin-up for the circumstellar matter around
several types of stars, i.e., post-AGB stars, B[e] stars, pre-main sequence
stars, and, in particular, the progenitor of Supernova 1987A.
