  To test the theoretical understanding that finding bright CO emission depends
primarily on dust shielding, we investigate the relationship between CO
emission ($I_{\rm CO}$) and the amount of dust (estimated from IR emission and
expressed as "$A_V$") across the Large Magellanic Cloud, the Small Magellanic
Cloud, and the Milky Way. We show that at our common resolution of 10 pc
scales, $I_{\rm CO}$ given a fixed line-of-sight $A_V$ is similar across all
three systems despite the difference in metallicity. We find some evidence for
a secondary dependence of $I_{\rm CO}$ on radiation field; in the LMC, $I_{\rm
CO}$ at a given $A_V$ is smaller in regions of high $T_{\rm dust}$, perhaps
because of an increased photodissociating radiation field. We suggest a simple
but useful picture in which the CO-to-H$_2$ conversion factor (\xco) depends on
two separable factors: (1) the distribution of gas column densities, which maps
to an extinction distribution via a dust-to-gas ratio; and (2) the dependence
of $I_{\rm CO}$ on $A_V$. Assuming that the probability distribution function
(PDF) of local Milky Way clouds is universal, this approach predicts a
dependence of \xco\ on $Z$ between $Z^{-1}$ and $Z^{-2}$ above about a third
solar metallicity. Below this metallicity, CO emerges from only the high column
density parts of the cloud and so depends very sensitively on the adopted PDF
and the H$_2$/{\sc Hi} prescription. The PDF of low metallicity clouds is thus
of considerable interest and the uncertainty associated with even an ideal
prescription for \xco\ at very low metallicity will be large.
