  Microlensing light curves are typically computed either by ray-shooting maps
or by contour integration via Green's theorem. We present an improved version
of the second method that includes a parabolic correction in Green's line
integral. In addition, we present an accurate analytical estimate of the
residual errors, which allows the implementation of an optimal strategy for the
contour sampling. Finally, we give a prescription for dealing with
limb-darkened sources reaching arbitrary accuracy. These optimizations lead to
a substantial speed-up of contour integration codes along with a full mastery
of the errors.
