  It has been reported that, within the hard-thermal-loop resummation scheme,
the production rate of soft real photons from a hot quark-gluon plasma exhibits
unscreened mass singularities. We show that still higher-order resummations
screen the mass singularities and obtain the finite soft-photon production rate
to leading order at logarithmic accuracy ${\cal O} (\alpha \alpha_s \ln^2
\alpha_s)$.
