Neurons in primary visual cortex (V1) are thought to receive inhibition from other V1 neurons selective for a variety of orientations. Evidence for this inhibition is commonly found in cross-orientation suppression: responses of a V1 neuron to optimally oriented bars are suppressed by superimposed mask bars of different orientation. We show, however, that suppression is unlikely to result from intracortical inhibition. First, suppression can be obtained with masks drifting too rapidly to elicit much of a response in cortex. Second, suppression is immune to hyperpolarization (through visual adaptation) of cortical neurons responding to the mask. Signals mediating suppression might originate in thalamus, rather than in cortex. Thalamic neurons exhibit some suppression; additional suppression might arise from depression at thalamocortical synapses. The mechanisms of suppression are subcortical and possibly include the very first synapse into cortex.