  We use the deepest and most complete redshift catalog currently available
(the Hubble Deep Field (HDF) North supplemented by new HDF South redshift data)
to minimize residuals between photometric and spectroscopic redshift estimates.
  The good agreement at z_spec < 1.5 shows that model libraries provide a good
description of the galaxy population. At z_spec > 2.0, the systematic shift
between photometric and spectroscopic redshifts decreases when the modeling of
the absorption by the interstellar and intergalactic media is refined. As a
result, in the entire redshift range 0 < z < 6, residuals between photometric
and spectroscopic redshifts are roughly halved. For objects fainter than the
spectroscopic limit, the main source of uncertainty in photometric redshifts is
related to photometric errors, and can be assessed with
  Monte Carlo simulations.
