  We point out that the nonlinear Schr{\"o}dinger lattice with a saturable
nonlinearity also admits staggered periodic as well as localized pulse-like
solutions. Further, the same model also admits solutions with a short period.
We examine the stability of these solutions and find that the staggered as well
as the short period solutions are stable in most cases. We also show that the
effective Peierls-Nabarro barrier for the pulse-like soliton solutions is zero.
