We examine models of the mass distribution for the first known case of grav
itational lensing. Several new sets of constraints are used, based on recen
t observations. We remodel the VLBI observations of the radio cores and jet
s in the two images of Q0957 + 561, showing that the previously derived pos
itions and uncertainties were incorrect. We use as additional constraints t
he candidate lensed pairs of galaxies discovered recently with the Hubble S
pace Telescope. We explore a wider range of lens models than before and fin
d 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 obse
rvations of the candidate lensed galaxies as well as direct measurements of
the cluster mass profile are needed before a useful value of the Hubble co
nstant can be derived from this lens.