In the companion study (C. Ripamonti et al., 2004), we present data that measure the effect of surface slant on perceived lightness. Observers are neither perfectly lightness constant nor luminance matchers, and there is considerable individual variation in performance. This work develops a parametric model that accounts for how each observer’s lightness matches vary as a function of surface slant. The model is derived from consideration of an inverse optics calculation that could achieve constancy. The inverse optics calculation begins with parameters that describe the illumination geometry. If these parameters match those of the physical scene, the calculation achieves constancy. Deviations in the model’s parameters from those of the scene predict deviations from constancy. We used numerical search to fit the model to each observer’s data. The model accounts for the diverse range of results seen in the experimental data in a unified manner, and examination of its parameters allows interpretation of the data that goes beyond what is possible with the raw data alone.