A widely used model of simultaneous luminance pattern masking is based on mechanisms that sum inputs linearly and produce a response that is an S-shaped function of that sum. This model makes two predictions about masking: (1) Changing the masker spatial waveform will shift the threshold-versus-masker contrast function horizontally by a multiplicative constant. (2) Adding a second fixed-contrast masker will shift this function horizontally by an additive constant. Experimental tests do not support these predictions. The results can be explained by a new model that incorporates broadband divisive inhibition, consistent with physiology.