  The frequency of microlensing planet detections, particularly in
difficult-to-model high-magnification events, is increasing. Their analysis can
require tens of thousands of processor hours or more, primarily because of the
high density and high precision of measurements whose modeling requires
time-consuming finite-source calculations. I show that a large fraction of
these measurements, those that lie at least one source diameter from a caustic
or the extension from a cusp, can be modeled using a very simple hexadecapole
approximation, which is one to several orders of magnitude faster than
full-fledged finite-source calculations. Moreover, by restricting the regions
that actually require finite-source calculations to a few isolated `caustic
features', the hexadecapole approximation will, for the first time, permit the
powerful `magnification-map' approach to be applied to events for which the
planet's orbital motion is important.
