  We present deep Magellan/Megacam stellar photometry of four recently
discovered faint Milky Way satellites: Sagittarius II (Sgr II), Reticulum II
(Ret II), Phoenix II (Phe II), and Tucana III (Tuc III). Our photometry reaches
~2-3 magnitudes deeper than the discovery data, allowing us to revisit the
properties of these new objects (e.g., distance, structural properties,
luminosity measurements, and signs of tidal disturbance). The satellite
color-magnitude diagrams show that they are all old (~13.5 Gyr) and metal-poor
([Fe/H]$\lesssim-2.2$). Sgr II is particularly interesting as it sits in an
intermediate position between the loci of dwarf galaxies and globular clusters
in the size-luminosity plane. The ensemble of its structural parameters is more
consistent with a globular cluster classification, indicating that Sgr II is
the most extended globular cluster in its luminosity range. The other three
satellites land directly on the locus defined by Milky Way ultra-faint dwarf
galaxies of similar luminosity. Ret II is the most elongated nearby dwarf
galaxy currently known for its luminosity range. Our structural parameters for
Phe II and Tuc III suggest that they are both dwarf galaxies. Tuc III is known
to be associated with a stellar stream, which is clearly visible in our
matched-filter stellar density map. The other satellites do not show any clear
evidence of tidal stripping in the form of extensions or distortions. Finally,
we also use archival HI data to place limits on the gas content of each object.
