  Recent observations of Wolf-Rayet (WR) binaries WR151 and WR155 infer that
their stellar winds are asymmetric. We show that such asymmetries can alter the
stellar-wind bubble structure, bringing the wind-termination shock closer to
the WR star. If the wind asymmetry is caused by rotation, the wind density and
distance to the wind-termination shock are both decreased along the rotation
axis by a factor of a few for the observed equator-to-pole wind density ratio
of WR151. If this asymmetry lasts until core-collapse the time taken to reach
the wind-termination shock by supernova ejecta or a gamma-ray burst jet is
reduced. This leads to a distorted structure of the supernova ejecta and makes
it more likely a constant density environment is inferred from gamma-ray burst
afterglow observations.
