  We report the discovery of a new star cluster, DES 3, in the constellation of
Indus, and deeper observations of the previously identified satellite DES
J0222.7$-$5217 (Eridanus III). DES 3 was detected as a stellar overdensity in
first-year Dark Energy Survey data, and confirmed with deeper photometry from
the 4.1 metre Southern Astrophysical Research (SOAR) telescope. The new system
was detected with a relatively high significance and appears in the DES images
as a compact concentration of faint blue point sources. We determine that DES 3
is located at a heliocentric distance of $\sim 76\,\mathrm{kpc}$ and it is
dominated by an old ($\simeq 9.8\,\mathrm{Gyr}$) and metal-poor
($\mathrm{[Fe/H]}\simeq -1.88$) population. While the age and metallicity
values of DES 3 are similar to globular clusters, its half-light radius
($r_\mathrm{h}\sim 6.5\,\mathrm{pc}$) and luminosity ($M_V \sim -1.9$) are more
indicative of faint star clusters. Based on the apparent angular size, DES 3,
with a value of $r_\mathrm{h}\sim 0.\!^{\prime}3$, is among the smallest faint
star clusters known to date. Furthermore, using deeper imaging of DES
J0222.7$-$5217 taken with the SOAR telescope, we update structural parameters
and perform the first isochrone modeling. Our analysis yields the first age
($\simeq 12.6\,\mathrm{Gyr}$) and metallicity ($\mathrm{[Fe/H]}\simeq -2.01$)
estimates for this object. The half-light radius ($r_\mathrm{h}\sim
10.5\,\mathrm{pc}$) and luminosity ($M_V\sim -2.7$) of DES J0222.7$-$5217
suggest that it is likely a faint star cluster. The discovery of DES 3
indicates that the census of stellar systems in the Milky Way is still far from
complete, and demonstrates the power of modern wide-field imaging surveys to
improve our knowledge of the Galaxy's satellite population.
