  I derive an upper limit to the distance to SN 1987A of $\dsn<46.77\pm
0.76\,\kpc$, or a distance modulus $\mu_\sn<18.350\pm 0.035$. If SN 1987A lies
in the plane of the Large Magellanic Cloud (LMC) and hence 500 pc in front of
the LMC center, this implies $\mu_\lmc<18.37\pm 0.04$. The determination rests
on a new measurement of the caustics in the ionized-emission light curves of
$t_-=75.0\pm 2.6\,$days and $t_+=390.0\pm 1.8\,$days. The estimate assumes that
the ring is circular. This assumption is shown to be consistent with the
available data and can be subjected to a future precise test. Moreover, I have
previously shown that modest deviations from circularity (eccentricities
$e<0.4$) affect the result by $<1\%$. The upper limit to the distance modulus
to M31 is $\mu_{\rm M31} < 24.43\pm 0.06$. If the response function of the
supernova-ring gas is prompt, then these upper limits become equalities.
