  We estimate the photon production rate from an SU(3) plasma at temperatures
of about 1.1Tc and 1.3Tc. Lattice results for the vector current correlator at
spatial momenta k ~ (2-6)T are extrapolated to the continuum limit and analyzed
with the help of a polynomial interpolation for the corresponding spectral
function, which vanishes at zero frequency and matches to high-precision
perturbative results at large invariant masses. For small invariant masses the
interpolation is compared with the NLO weak-coupling result, hydrodynamics, and
a holographic model. At vanishing invariant mass we extract the photon rate
which for k \gsim 3T is found to be close to the NLO weak-coupling prediction.
For k \lsim 2T uncertainties remain large but the photon rate is likely to fall
below the NLO prediction, in accordance with the onset of a strongly
interacting behaviour characteristic of the hydrodynamic regime.
