  Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of
cubic-quintic and full saturable models are studied, starting from the full
system of the Maxwell's equations, rather than from the paraxial (NLS)
approximation. For the solitons with both TE and TM polarizations, it is shown
that there always exists a finite minimum width, and they cease to exist at a
critical value of the propagation constant, at which their width diverges. Full
similarity of the results obtained for both nonlinearities suggests that the
same general conclusions apply to narrow solitons in any non-Kerr model.
