We describe an empirical investigation of departures from Lambert's law for rough and shiny surfaces. We commence by using a recently reported method to recover estimates of the surface radiance function for objects illuminated in the viewer direction. This method is nonparametric, and offers the advantage that it is simple to use since it does not require detailed camera calibration. We compare the radiance data with a number of phenomenological and physics-based reflectance models. The models studied include those of Oren-Nayar, Wolff and different variants of the Beckmann model. The main conclusion of the study is that among these models the best fit to the empirical data is found to be the Wolff model for smooth objects and the modified Beckmann model for rough objects.