We present the discovery of three new Milky Way satellites from our search for compact stellar overdensities in the photometric catalog of the Panoramic Survey Telescope and Rapid Response System 1 (Pan-STARRS 1, or PS1) 3π survey. The first satellite, Laevens 3, is located at a heliocentric distance of d = 67 ± 3 kpc. With a total magnitude of MV = -4.4 ± 0.3 and a half-light radius of rh = 7 ± 2 pc, its properties resemble those of outer halo globular clusters. The second system, Draco II/Laevens 4, is a closer and fainter satellite (d ∼ 20 kpc, MV = -2.9 ± 0.8), whose uncertain size (rh = 19-6+8) renders its classification difficult without kinematic information; it could either be a faint and extended globular cluster or a faint and compact dwarf galaxy. The third satellite, Sagittarius II/Laevens 5 (Sgr II), has an ambiguous nature, as it is either the most compact dwarf galaxy or the most extended globular cluster in its luminosity range (rh = 37-8+9 and MV = -5.2 ± 0.4). At a heliocentric distance of 67 ± 5 kpc, this satellite lies intriguingly close to the expected location of the trailing arm of the Sagittarius stellar stream behind the Sagittarius dwarf spheroidal galaxy (Sgr dSph). If confirmed through spectroscopic follow up, this connection would locate this part of the trailing arm of the Sagittarius stellar stream that has so far gone undetected. It would further suggest that Sgr II was brought into the Milky Way halo as a satellite of the Sgr dSph.