  The profiles of narrow lattice solitons are calculated analytically using
perturbation analysis. A stability analysis shows that solitons centered at a
lattice (potential) maximum are unstable, as they drift toward the nearest
lattice minimum. This instability can, however, be so weak that the soliton is
``mathematically unstable'' but ``physically stable''. Stability of solitons
centered at a lattice minimum depends on the dimension of the problem and on
the nonlinearity. In the subcritical and supercritical cases, the lattice does
not affect the stability, leaving the solitons stable and unstable,
respectively. In contrast, in the critical case (e.g., a cubic nonlinearity in
two transverse dimensions), the lattice stabilizes the (previously unstable)
solitons. The stability in this case can be so weak, however, that the soliton
is ``mathematically stable'' but ``physically unstable''.
