  We amalgamate the many experimental limits on the $ab\anti b$ coupling of a
light CP-odd Higgs boson, $a$, including model-dependence coming from the ratio
of the $at\anti t$ to the $a b\anti b$ coupling. We then employ these limits to
analyze the extent to which a light $a$ can make a significant contribution to
the discrepancy, $\Delta a_\mu$, between the experimentally observed $a_\mu$
and that predicted by the standard model. In a "model-independent" framework
and in the context of a general two-Higgs-doublet model this is a significant
possibility. In contrast, the minimal supersymmetric model is too strongly
constrained (after combining experimental and theoretical input) to allow a
CP-odd-$a$ explanation of $\Delta a_\mu$. The next-to-minimal supersymmetric
model allows more freedom and the light $a$ of the model could explain the full
$\Delta a_\mu$ if $9.2\gev<\ma<12\gev $, or contribute substantially for larger
$\ma$, if $\tanb$ is large.
