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-m 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 ≃76.2 kpc and it is dominated by an old (≃9.8 Gyr) and metal-poor ([Fe/H] ≃ −1.84) population. While the age and metallicity values of DES 3 are comparable to typical globular clusters (objects with a high stellar density, stellar mass of ∼105 M⊙ and luminosity MV ∼ −7.3), its half-light radius (rh ∼ 6.87 pc) and luminosity (MV ∼ −1.7) are more indicative of faint star cluster. Based on the angular size, DES 3, with a value of rh ∼ 0′.31, 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 modelling. Our analysis yields the first age (≃12.6 Gyr) and metallicity ([Fe/H] ≃ −2.01) estimates for this object. The half-light radius (rh ≃ 11.24 pc) and luminosity (MV ≃ −2.4) 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.