A simplified geometric-optical model (SGM) was inverted using red band reflectance data acquired at 275 m in nine viewing angles from the Multiangle Imaging SpectroRadiometer (MISR) flown on NASA's Terra satellite, to provide estimates of fractional woody plant cover for large areas (over 3519 km2) in parts of the Chihuahuan Desert in New Mexico, USA. The use of the model in these semi-arid environments was enabled by the derivation of a priori estimates of the soil/understory background reflectance response. This was made possible by determining relationships between the kernel weights from a LiSparse-RossThin model adjusted against the same MISR data -- together with spectral reflectance data derived from MISR's nadir-viewing camera -- and the parameters of the Walthall model used to represent the background. Spatial distributions of retrieved fractional woody plant cover match those of % tree cover in the global MODIS Vegetation Continuous Fields product but also include shrubs. Good relationships were obtained with fractional shrub cover measured in pastures in the USDA, ARS Jornada Experimental Range but tree cover in higher elevation and riparian zones was dramatically over-estimated as a result of the fixing of crown height and shape parameters.