  The curvature of a relativistic blast wave implies that its emission arrives
to observers with a spread in time. This effect is believed to wash out fast
variability in the lightcurves of GRB afterglows. We note that the spreading
effect is reduced if emission is anisotropic in the rest-frame of the blast
wave (i.e. if emission is limb-brightened or limb-darkened). In particular,
synchrotron emission is almost certainly anisotropic, and may be strongly
anisotropic, depending on details of electron acceleration in the blast wave.
Anisotropic afterglows can display fast and strong variability at high
frequencies (above the 'fast-cooling' frequency). This may explain the
existence of bizarre features in the X-ray afterglows of GRBs, such as sudden
drops and flares. We also note that a moderate anisotropy can significantly
delay the 'jet break' in the lightcurve, which makes it harder to detect.
