The responses of neurons in the primary visual cortex (V1) to an optimally-oriented grating are suppressed when a non-optimal grating is superimposed. Although cross-orientation suppression is thought to reflect mechanisms that maintain a distributed code for orientation, the impact of superimposed gratings upon V1 populations is unknown. Using intrinsic signal optical imaging, we find that patterns of tree shrew V1 activity evoked by superimposed equal-contrast gratings were predicted by the mean of patterns evoked by individual component gratings. This prediction held across contrasts, for summed sinusoidal gratings or non-summing square-wave gratings, and was reflected in single-unit extracellular recordings. Intracellular recordings revealed consistent levels of suppression throughout the evolution of subthreshold responses. These results indicate that divisive suppression powerfully governs population responses to multiple orientations. Moreover, the specific form of suppression we observe appears to support independent population codes for stimulus orientation and strength, and calls for a reassessment of mechanisms that underlie cross-orientation suppression.