Two orthogonal patterns presented to the two eyes, respectively, are perceived as alternating in time, a phenomenon often assumed to reflect competition between neuronal activities corresponding to the two eyes, presumably in the primary visual cortex. Recent evidence supports a competition between neuronal activities corresponding to the two patterns (objects) at some higher cortical processing stage after inputs from the two eyes have converged. Here, using textures made of Gabor signals, we present psychophysical data showing that the level of visual processing at which competition takes place and is resolved, is determined by the degree of stimulus coherence. Moreover, depending on stimulus parameters, competition may occur at several levels of processing at the same time.