  We revisit the constraints on evaporating primordial black holes (PBHs) from
the isotropic X-ray and soft gamma-ray background in the mass range
$10^{16}-10^{18}$ g. We find that they are stronger than usually inferred due
to two neglected effects: i) The contribution of the annihilation radiation due
to positrons emitted in the evaporation process. ii) The high-latitude,
Galactic contribution to the measured isotropic flux. We study the dependence
of the bounds from the datasets used, the positron annihilation conditions, and
the inclusion of the astrophysical background. We derive competitive bounds
excluding non-spinning PBH with monochromatic mass function as the totality of
dark matter for masses below about 1.6$\times 10^{17}\,$g. We also show that
the inclusion of spin and/or an extended, log-normal mass function lead to
tighter bounds. Our study suggests that the isotropic flux is an extremely
promising target for future missions in improving the sensitivity to PBHs as
candidates for dark matter.
