  Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable
nonlinearity are reported. For finite lattices we find two different
standing-wave-like solutions, and for an infinite lattice we find a localized
soliton-like solution. The existence requirements and stability of these
solutions are discussed, and we find that our solutions are linearly stable in
most cases. We also show that the effective Peierls-Nabarro barrier potential
is nonzero thereby indicating that this discrete model is quite likely
nonintegrable.
