  All of the proposed explanations for the microlensing events observed towards
the LMC have difficulties. One of these proposed explanations, LMC
self-lensing, which invokes ordinary LMC stars as the long sought-after lenses,
has recently gained considerable popularity as a possible solution to the
microlensing conundrum. In this paper, we carefully examine the set of LMC
self-lensing models. In particular, we review the pertinent observations made
of the LMC, and show how these observations place limits on such self-lensing
models. We find that, given current observational constraints, no purely LMC
disk models are capable of producing optical depths as large as that reported
in the MACHO collaboration 2-year analysis. Besides pure disk, we also consider
alternate geometries, and present a framework which encompasses the previous
studies of LMC self-lensing. We discuss which model parameters need to be
pushed in order for such models to succeed. For example, like previous workers,
we find that an LMC halo geometry may be able to explain the observed events.
However, since all known LMC tracer stellar populations exhibit disk-like
kinematics, such models will have difficulty being reconciled with
observations. For SMC self-lensing, we find predicted optical depths differing
from previous results, but more than sufficient to explain all observed SMC
microlensing. In contrast, for the LMC we find a self-lensing optical depth
contribution between 0.47e-8 and 7.84e-8, with 2.44e-8 being the value for the
set of LMC parameters most consistent with current observations.
