  We investigate analytically the effect of an anisotropic distribution of the
kinetic energy within a relativistic fireball on the decay of the afterglow
emission, focusing on axially symmetric fireballs with a uniform core and a
power-law decrease with angle outside the core. The afterglow fall-off steepens
after the core becomes fully visible. For observer directions within the core,
simple formulae are derived for the afterglow decay after the break, while for
off-core observers results are shown graphically. Some criteria for assessing
from observations the necessity of an angular structure and/or collimation are
given. Applying them to several afterglows with light-curve breaks, we find
that jets endowed with structure are required only if the circumburst medium
has a wind-like (r^{-2}) stratification. Numerical fits to the multiwavelength
emission of the afterglows 990510 and 000301c show that, for the former, the
angular distribution of the ejecta kinetic energy is not far from uniformity,
and that, with a standard power-law electron distribution, the sharp steepening
of the R-band light-curve of the latter is better accommodated by a structured
jet than an uniform outflow. Structured outflows may accommodate the shallower
light-curve breaks observed in other afterglows.
