  We examine models of the mass distribution for the first known case of
gravitational lensing. Several new sets of constraints are used, based on
recent observations. We remodel the VLBI observations of the radio jets in the
two images of Q0957+561, showing that the previously derived positions and
uncertainties were incorrect. We use as additional constraints the candidate
lensed pairs of galaxies identified recently with the Hubble Space Telescope.
We explore a wider range of lens models than before, and find that the Hubble
constant is not tightly constrained once elliptical lens models are considered.
We also discuss the systematic uncertainties caused by the cluster containing
the lens galaxy. We conclude that additional observations of the candidate
lensed galaxies as well as direct measurements of the cluster mass profile are
needed before an accurate value of the Hubble constant can be derived from this
lens.
