  The Hawking evaporation process, leading to the production of detectable
particle species, constrains the abundance of light black holes, presumably of
primordial origin. Here, we reconsider and correct constraints from soft
gamma-ray observations, including of the gamma-ray line, at 511 keV, produced
by electron-positron pair-annihilation, where positrons originate from black
hole evaporation. First, we point out that the INTEGRAL detection of the Large
Magellanic Cloud provides one of the strongest bounds attainable with present
observations; and that future MeV gamma-ray telescopes, such as GECCO, will
greatly enhance such constraints. Second, we discuss issues with previous
limits from the isotropic flux at 511 keV and we provide updated, robust
constraints from recent measurements of the diffuse Galactic soft gamma-ray
emission and from the isotropic soft gamma-ray background.
