In previous studies, desert-fringe vegetation densities were assessed in an ungrazed semi-arid rangeland in Utah and in an animal exclosure in the arid Sinai. Applying satellite measurements of reflectances, the dark vertical cylinders (DVC) model for desert-scrub (characterized by predominantly vertical architecture) was inverted. In the present study a new plane-parallel model is presented, which treats the canopy as a layer of small Lambertian spheres (SLS), or small facets (leaves) with a specific distribution of the leaf area, where the Schonberg function of the angle between the solar beam and the view direction specifies the reflectance from the canopy. The SLS model is inverted with the satellite-measured reflectances of the Sinai exclosure and the surrounding overgrazed, practically bare-soil terrain. The SLS-model inversion results are compared with DVC results. Both models provide plausible canopy characterizations, but the SLS model is more realistic when viewing from the zenith with sun at a high elevation. The reflectance ratio of the dark plant-elements to the bright soil is key to assessing the density of the plants. In the inversion of the AVHRR visible and near-infrared data, the plant element reflectances in the infrared are adjusted so that the plant optical density in the infrared matches that determined in the visible spectral region. Early in the dry summer season (after the winter rains), high infrared reflectances are inferred, but sharply lower infrared reflectances, appropriate for the dried out plants, are found in the later stages of the dry season. This result, that the physical changes in the plant conditions can be assessed, is highly encouraging for our SLS modeling effort.