Optical Limiters which operate by exploiting nonlinear absorption and nonlinear refraction are most effective towards an incoming laser beam when the active material is somewhat thicker than one Rayleigh length. A variety of thick optical limiter configurations are described and modeled by appropriately integrating the formulas for thin nonlinear media with gaussian-shaped beams. The attenuating effects of linear losses are allowed for, and the approach is exact to the first order in optical power or irradiance. Irradiance-dependent and fluence-dependent absorbers are considered. For a gaussian-shaped input beam, we find that the combined effects of diffraction and nonlinear absorption produce, in the thick-medium limit, a transmitted beam which retains a gaussian-shaped profile at the far field, but which is now uniformly attenuated according to the magnitudes of the nonlinear and linear absorption parameters. This implies that the normalized transmittance is independent of the size of the receiving aperture. As the optical beam power increases the limiting behaviour saturates. We have discovered a simple saturation formula which agrees well with numerically calculated transmittances for thick irradiance-dependent absorbers within the strongly nonlinear regime. Under certain conditions this formula also describes the behaviour of refractive limiters, providing a simple and accurate technique for modeling limiters over a broad parameter range.