  We present a method to analyze binary-lens microlensing light curves with one
well-sampled fold caustic crossing. In general, the surface of chi^2 shows
extremely complicated behavior over the 9-parameter space that characterizes
binary lenses. This makes it difficult to systematically search the space and
verify that a given local minimum is a global minimum. We show that for events
with well-monitored caustics, the caustic-crossing region can be isolated from
the rest of the light curve and easily fit to a 5-parameter function. Four of
these caustic-crossing parameters can then be used to constrain the search in
the larger 9-parameter space. This allows a systematic search for all solutions
and thus identification of all local minima. We illustrate this technique using
the PLANET data for MACHO 98-SMC-1, an excellent and publicly available
caustic-crossing data set. We show that a very broad range of parameter
combinations are compatible with the PLANET data set, demonstrating that
observations of binary-lens lightcurves with sampling of only one caustic
crossing do not yield unique solutions. The corollary to this is that the time
of the second caustic crossing cannot be reliably predicted on the basis of
early data including the first caustic crossing alone. We investigate the
requirements for determination of a unique solution and find that occasional
observations of the first caustic crossing may be sufficient to derive a
complete solution.
